<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JULY 17, 1998
 
                                           REGISTRATION NO. 333-
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                    FORM S-8
 
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                             ---------------------
                                SOUTHDOWN, INC.
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                  LOUISIANA                                      72-0296500
       (State or other jurisdiction of                        (I.R.S. Employer
        incorporation or organization)                      Identification No.)
        1200 SMITH STREET, SUITE 2400                              77002
                HOUSTON, TEXAS                                   (Zip Code)
   (Address of Principal Executive Offices)
               SOUTHDOWN, INC.                               MEDUSA CORPORATION
            1989 STOCK OPTION PLAN                     1991 LONG-TERM INCENTIVE PLAN
             (Full title of plan)                           (Full title of plan)
</TABLE>
 
                               PATRICK S. BULLARD
                VICE PRESIDENT -- GENERAL COUNSEL AND SECRETARY
                                SOUTHDOWN, INC.
                         1200 SMITH STREET, SUITE 2400
                              HOUSTON, TEXAS 77002
                    (Name and address of agent for service)
 
                                 (713) 650-6200
         (Telephone number, including area code, of agent for service)
                             ---------------------
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------
                                                     PROPOSED MAXIMUM      PROPOSED MAXIMUM
  TITLE OF SECURITIES          AMOUNT TO BE           OFFERING PRICE      AGGREGATE OFFERING        AMOUNT OF
    TO BE REGISTERED            REGISTERED              PER SHARE               PRICE           REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------
<S>                      <C>                       <C>                  <C>                    <C>
Common Stock, $1.25 par
value(1)................  3,000,000 shares(2)(3)       $70.5315(4)         $211,594,500(4)         $62,421(2)
------------------------------------------------------------------------------------------------------------------
Common Stock $1.25 par
  value(1)..............       521,752(3)(5)           $70.5315(4)         $ 36,799,952(4)           $10,856
------------------------------------------------------------------------------------------------------------------
          Total.........    3,521,752 shares(3)        $70.5315(4)         $248,394,452(4)         $73,277(2)
------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------
</TABLE>
 
(1) Includes the Preferred Stock Purchase Rights issuable pursuant to the Rights
    Agreement dated as of March 4, 1991, between the Registrant and ChaseMellon
    Shareholder Services, Inc. As no separate consideration is payable with
    respect to the Preferred Stock Purchase Rights, the registration fee with
    respect to such securities is included in the registration fee for the
    Common Stock.
 
(2) The 3,000,000 shares are in addition to the 2,000,000 shares initially
    available under the Southdown, Inc. 1989 Stock Option Plan which have been
    previously registered under the Securities Act of 1933, as amended (the
    "Securities Act") pursuant to the registration statement referred to in the
    final paragraph on this facing page, 252,895 of which shares have not yet
    been issued. A filing fee of $1,835.42 was previously paid by registrant
    with respect to such 252,895 shares.
 
(3) Pursuant to Rule 416 under the Securities Act, includes any additional
    shares issued pursuant to the antidilution provisions of the plan.
 
(4) Estimated solely for the purpose of determining the registration fee and
    calculated pursuant to Rule 457(c) and (h) by reference to the average of
    the high and low sales prices of the Common Stock on the New York Stock
    Exchange on July 15, 1998, which was $70.5315 per share.
 
(5) The 521,752 shares of Common Stock are issuable under the Medusa Corporation
    1991 Long-Term Incentive Plan, which was adopted by Southdown, Inc. in
    connection with the merger of a wholly-owned subsidiary of Southdown, Inc.
    into Medusa Corporation on June 30, 1998, pursuant to which Medusa
    Corporation became a wholly-owned subsidiary of Southdown, Inc.
 
     THE DOCUMENTS SENT OR GIVEN TO EMPLOYEES IN CONNECTION WITH THE SOUTHDOWN,
INC. 1989 STOCK OPTION PLAN AS DESCRIBED IN PART I OF THIS REGISTRATION
STATEMENT AND THE OTHER DOCUMENTS WHICH TOGETHER THEREWITH CONSTITUTE THE
PROSPECTUS MEETING THE REQUIREMENTS OF SECTION 10(A) OF THE SECURITIES ACT
CONSTITUTE, PURSUANT TO RULE 429 UNDER THE SECURITIES ACT, A COMBINED PROSPECTUS
THAT ALSO RELATES TO 252,895 SHARES OF COMMON STOCK REGISTERED ON FORM S-8,
REGISTRATION NO. 33-35011, WHICH BECAME EFFECTIVE ON JUNE 15, 1990.
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
<PAGE>   2
 
                                     PART I
 
              INFORMATION REQUIRED IN THE SECTION 10(A) PROSPECTUS
 
     The documents containing the information specified in Part I will be sent
or given to employees as specified by Rule 428(b). In accordance with the
instructions to Part I of Form S-8, such documents are not being filed and will
not be filed with the Securities and Exchange Commission (the "Commission"),
either as part of this registration statement or as a prospectus or prospectus
supplement pursuant to Rule 424.
 
                                    PART II
 
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
 
ITEM 3. INCORPORATION OF DOCUMENTS BY REFERENCE.
 
     The following documents, or portions of documents, previously filed by
Southdown, Inc. (the "Company") with the Commission are hereby incorporated
herein by reference:
 
          (a)  The Company's Annual Report on Form 10-K for the year ended
     December 31, 1997, as amended by Form 10-K/A filed on April 27, 1998;
 
          (b)  The Company's Quarterly Report on Form 10-Q for the quarter ended
     March 31, 1998;
 
          (c)  The Company's Current Report on Form 8-K filed on March 18, 1998,
     as amended by Form 8-K/A filed on April 10, 1998;
 
          (d)  The Company's Current Report on Form 8-K filed on June 18, 1998;
 
          (e)  The Company's Current Report on Form 8-K filed on July 15, 1998;
     and
 
          (f)  The Company's Registration Statement on Form 8-C relating to the
     Company's Common Stock and its Registration Statement on Form 8-A relating
     to the Company's Preferred Stock Purchase Rights, each as amended to date.
 
     All reports and other documents filed by the Company with the Commission
pursuant to Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act
of 1934, as amended, after the date of this Registration Statement and prior to
the termination of the offering of securities made hereby shall be deemed to be
incorporated by reference herein and to be a part hereof from the respective
dates of filing of such reports and other documents, other than the portions of
such documents which by statute, by designation in such documents or otherwise
are not required to be filed with the Commission or are not required to be
incorporated herein by reference. Any statement contained herein or in a
document incorporated or deemed to be incorporated by reference herein shall be
deemed to be modified or superseded for all purposes to the extent that a
statement contained in any other subsequently filed document that is also
incorporated or deemed to be incorporated by reference herein modifies or
supersedes such statement. Any such statement so modified or superseded shall
not be deemed, except as so modified or superseded, to constitute a part of this
Registration Statement.
 
ITEM 4. DESCRIPTION OF SECURITIES.
 
     Not applicable.
 
ITEM 5. INTERESTS OF NAMED EXPERTS AND COUNSEL.
 
     Not applicable.
 
ITEM 6. INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     The Louisiana Business Corporation Law ("LBCL") generally gives a
corporation the power to indemnify any of its directors or officers against
certain expenses, judgments, fines and amounts paid in
 
                                        2
<PAGE>   3
 
settlement in connection with certain actions, suits or proceedings, provided
generally that such person acted in good faith and in a manner he reasonably
believed to be in or not opposed to the interests of the corporation and, with
respect to any criminal action or proceeding, had no reasonable cause to believe
his conduct was unlawful. In the case of an action by, or in the right of, the
corporation, the corporation may indemnify such person against expenses,
including attorneys' fees and amounts paid in settlement not exceeding, in the
judgment of the board of directors, the estimated expense of litigating the
action to conclusion, actually and reasonably incurred in connection with the
defense or settlement of such action, and no indemnification shall be made in
respect of any claim, issue, or matter as to which such person shall have been
adjudged by a court of competent jurisdiction, after exhaustion of all appeals
therefrom, to be liable for willful or intentional misconduct in the performance
of his duty to the corporation, unless, and only to the extent that the court
shall determine upon application that, despite the adjudication of liability but
in view of all the circumstances of the case, he is fairly and reasonably
entitled to indemnity for such expenses which the court shall deem proper.
 
     Indemnification provided pursuant to the foregoing provisions is not, under
the LBCL, deemed exclusive of any other rights to which the person indemnified
is entitled under any bylaw, agreement, authorization of shareholders or
directors; however, no such other indemnification measure shall permit
indemnification of any person for the results of such person's willful or
intentional misconduct. In addition, the LBCL contains provisions to the general
effect that any director shall in the performance of his duties be fully
protected in relying in good faith upon the records of the corporation and upon
such information, opinions, reports or statements presented to the corporation,
the board of directors, or any committee thereof by any of the corporation's
officers or employees, or by any committee of the board of directors, or by any
counsel, appraiser, engineer (including a petroleum reservoir engineer), or
independent or certified public accountant selected by the board of directors or
any committee thereof with reasonable care, or by any other person as to matters
the director reasonably believes are within such other person's professional or
expert competence and which person is selected by the board of directors or any
committee thereof with reasonable care. A director shall not be liable for the
commission of a prohibited act if his dissent was either noted in the minutes of
the meetings or filed promptly thereafter in the registered office of the
corporation.
 
     As permitted under Section 24(C)(4) of the LBCL, Article XIII of the
Restated Articles of Incorporation of the Company eliminates the personal
liability of any director or officer to the Company or its shareholders for
monetary damages for breach of fiduciary duty in such capacity, except for (i)
any breach of the duty of loyalty to the Company or its shareholders; (ii) acts
or omissions not in good faith or involving intentional misconduct or a knowing
violation of law; (iii) unlawful payment of dividends or unlawful stock purchase
or redemption; or (iv) any transaction from which the director or officer
derived an improper personal benefit.
 
     Article VI, Section 6 of the Company's Bylaws contemplates that the Company
shall indemnify its directors and officers to the maximum extent permitted by
Louisiana law.
 
     In addition, the Company has purchased a liability insurance policy under
which its directors and officers are indemnified against certain losses arising
from certain claims that may be made against them by reason of their serving in
such capacity.
 
ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED.
 
     Not applicable.
 
                                        3
<PAGE>   4
 
ITEM 8. EXHIBITS.
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
          3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
</TABLE>
 
---------------
 
* Incorporated by reference
 
ITEM 9. UNDERTAKINGS.
 
     (a) The undersigned registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this registration statement:
 
             (i) To include any prospectus required by section 10(a)(3) of the
        Securities Act of 1933 (the "Securities Act");
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of the registration statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in the registration statement;
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in the registration statement
        or any material change to such information in the registration
        statement;
 
     Provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) above shall not
     apply if the information required to be included in a post-effective
     amendment by those paragraphs is contained in periodic reports filed with
     or furnished to the Commission by the registrant pursuant to Section 13 or
     Section 15(d) of the Securities Exchange Act of 1934 (the "Exchange Act")
     that are incorporated by reference in this Registration Statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act, each such post-effective amendment shall be deemed to be a
     new registration statement relating to the securities offered therein, and
     the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.
 
                                        4
<PAGE>   5
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
registrant's annual report pursuant to section 13(a) or section 15(d) of the
Exchange Act that is incorporated by reference in the registration statement
shall be deemed to be a new registration statement relating to the securities
offered therein, and the offering of such securities at that time shall be
deemed to be the initial bona fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act may be permitted to directors, officers and controlling persons of the
registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                        5
<PAGE>   6
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, State of Texas, on the 17th day of July,
1998.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
                                              ----------------------------------
                                                      Clarence C. Comer
                                                President and Chief Executive
                                                            Officer
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
<C>                                                     <S>                                <C>
 
                /s/ CLARENCE C. COMER                   President and Chief Executive         July 17, 1998
-----------------------------------------------------     Officer and Director (Principal
                  Clarence C. Comer                       Executive Officer)
 
                 /s/ DENNIS M. THIES                    Executive Vice President --           July 17, 1998
-----------------------------------------------------     Finance and Chief Financial
                   Dennis M. Thies                        Officer (Principal Financial
                                                          Officer)
 
                /s/ ALLAN B. KORSAKOV                   Vice President and Corporate          July 17, 1998
-----------------------------------------------------     Controller (Principal Accounting
                  Allan B. Korsakov                       Officer)
 
                   /s/ R. S. EVANS                      Director                              July 17, 1998
-----------------------------------------------------
                     R. S. Evans
 
              /s/ KILLIAN L. HUGER, JR.                 Director                              July 17, 1998
-----------------------------------------------------
                Killian L. Huger, Jr.
 
                /s/ ROBERT G. POTTER                    Director                              July 17, 1998
-----------------------------------------------------
                  Robert G. Potter
 
                  /s/ FRANK J. RYAN                     Director                              July 17, 1998
-----------------------------------------------------
                    Frank J. Ryan
 
                 /s/ WHITSON SADLER                     Director                              July 17, 1998
-----------------------------------------------------
                   Whitson Sadler
 
                /s/ ROBERT J. SLATER                    Director                              July 17, 1998
-----------------------------------------------------
                  Robert J. Slater
</TABLE>
 
                                        6
<PAGE>   7
 
<TABLE>
<CAPTION>
                      SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
<C>                                                     <S>                                <C>
 
              /s/ DAVID J. TIPPECONNIC                  Director                              July 17, 1998
-----------------------------------------------------
                David J. Tippeconnic
 
                /s/ J. BRUCE TOMPKINS                   Director                              July 17, 1998
-----------------------------------------------------
                  J. Bruce Tompkins
 
              /s/ GEORGE E. UDING, JR.                  Director                              July 17, 1998
-----------------------------------------------------
                George E. Uding, Jr.
 
               /s/ V. H. VAN HORN, III                  Director                              July 17, 1998
-----------------------------------------------------
                 V. H. Van Horn, III
 
               /s/ STEVEN B. WOLITZER                   Director                              July 17, 1998
-----------------------------------------------------
                 Steven B. Wolitzer
</TABLE>
 
                                        7
<PAGE>   8
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
 
          3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
</TABLE>
 
---------------
 
* Incorporated by reference
 
                                        8
[{"type": "S-8", "sequence": "1", "description": "SOUTHDOWN, INC.", "secsgml_size_bytes": 26092}]
{"company-data": {"conformed-name": "SOUTHDOWN INC", "cik": "0000313058", "assigned-sic": "3241", "irs-number": "720296500", "state-of-incorporation": "LA", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-59349", "film-number": "98668213"}, "business-address": {"street1": "1200 SMITH ST STE 2400", "city": "HOUSTON", "state": "TX", "zip": "77002", "phone": "7136506200"}, "mail-address": {"street1": "1200 SMITH STREET SUITE 2400", "city": "HOUSTON", "state": "TX", "zip": "77002"}}
1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JULY 17, 1998
 
                                           REGISTRATION NO. 333-
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                    FORM S-8
 
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933
                             ---------------------
                                SOUTHDOWN, INC.
             (Exact name of registrant as specified in its charter)
LOUISIANA                                      72-0296500
       (State or other jurisdiction of                        (I.R.S. Employer
        incorporation or organization)                      Identification No.)
        1200 SMITH STREET, SUITE 2400                              77002
                HOUSTON, TEXAS                                   (Zip Code)
   (Address of Principal Executive Offices)
               SOUTHDOWN, INC.                               MEDUSA CORPORATION
            1989 STOCK OPTION PLAN                     1991 LONG-TERM INCENTIVE PLAN
             (Full title of plan)                           (Full title of plan)
PATRICK S. BULLARD
                VICE PRESIDENT -- GENERAL COUNSEL AND SECRETARY
                                SOUTHDOWN, INC.
                         1200 SMITH STREET, SUITE 2400
                              HOUSTON, TEXAS 77002
                    (Name and address of agent for service)
 
                                 (713) 650-6200
         (Telephone number, including area code, of agent for service)
                             ---------------------
                        CALCULATION OF REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------
                                                     PROPOSED MAXIMUM      PROPOSED MAXIMUM
  TITLE OF SECURITIES          AMOUNT TO BE           OFFERING PRICE      AGGREGATE OFFERING        AMOUNT OF
    TO BE REGISTERED            REGISTERED              PER SHARE               PRICE           REGISTRATION FEE
------------------------------------------------------------------------------------------------------------------
Common Stock, $1.25 par
value(1)................  3,000,000 shares(2)(3)       $70.5315(4)         $211,594,500(4)         $62,421(2)
------------------------------------------------------------------------------------------------------------------
Common Stock $1.25 par
  value(1)..............       521,752(3)(5)           $70.5315(4)         $ 36,799,952(4)           $10,856
------------------------------------------------------------------------------------------------------------------
          Total.........    3,521,752 shares(3)        $70.5315(4)         $248,394,452(4)         $73,277(2)
------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------
(1) Includes the Preferred Stock Purchase Rights issuable pursuant to the Rights
    Agreement dated as of March 4, 1991, between the Registrant and ChaseMellon
    Shareholder Services, Inc. As no separate consideration is payable with
    respect to the Preferred Stock Purchase Rights, the registration fee with
    respect to such securities is included in the registration fee for the
    Common Stock.
 
(2) The 3,000,000 shares are in addition to the 2,000,000 shares initially
    available under the Southdown, Inc. 1989 Stock Option Plan which have been
    previously registered under the Securities Act of 1933, as amended (the
    "Securities Act") pursuant to the registration statement referred to in the
    final paragraph on this facing page, 252,895 of which shares have not yet
    been issued. A filing fee of $1,835.42 was previously paid by registrant
    with respect to such 252,895 shares.
 
(3) Pursuant to Rule 416 under the Securities Act, includes any additional
    shares issued pursuant to the antidilution provisions of the plan.
 
(4) Estimated solely for the purpose of determining the registration fee and
    calculated pursuant to Rule 457(c) and (h) by reference to the average of
    the high and low sales prices of the Common Stock on the New York Stock
    Exchange on July 15, 1998, which was $70.5315 per share.
 
(5) The 521,752 shares of Common Stock are issuable under the Medusa Corporation
    1991 Long-Term Incentive Plan, which was adopted by Southdown, Inc. in
    connection with the merger of a wholly-owned subsidiary of Southdown, Inc.
    into Medusa Corporation on June 30, 1998, pursuant to which Medusa
    Corporation became a wholly-owned subsidiary of Southdown, Inc.
 
     THE DOCUMENTS SENT OR GIVEN TO EMPLOYEES IN CONNECTION WITH THE SOUTHDOWN,
INC. 1989 STOCK OPTION PLAN AS DESCRIBED IN PART I OF THIS REGISTRATION
STATEMENT AND THE OTHER DOCUMENTS WHICH TOGETHER THEREWITH CONSTITUTE THE
PROSPECTUS MEETING THE REQUIREMENTS OF SECTION 10(A) OF THE SECURITIES ACT
CONSTITUTE, PURSUANT TO RULE 429 UNDER THE SECURITIES ACT, A COMBINED PROSPECTUS
THAT ALSO RELATES TO 252,895 SHARES OF COMMON STOCK REGISTERED ON FORM S-8,
REGISTRATION NO. 33-35011, WHICH BECAME EFFECTIVE ON JUNE 15, 1990.
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
2
 
                                     PART I
 
              INFORMATION REQUIRED IN THE SECTION 10(A) PROSPECTUS
 
     The documents containing the information specified in Part I will be sent
or given to employees as specified by Rule 428(b). In accordance with the
instructions to Part I of Form S-8, such documents are not being filed and will
not be filed with the Securities and Exchange Commission (the "Commission"),
either as part of this registration statement or as a prospectus or prospectus
supplement pursuant to Rule 424.
 
                                    PART II
 
               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT
 
ITEM 3. INCORPORATION OF DOCUMENTS BY REFERENCE.
 
     The following documents, or portions of documents, previously filed by
Southdown, Inc. (the "Company") with the Commission are hereby incorporated
herein by reference:
 
          (a)  The Company's Annual Report on Form 10-K for the year ended
     December 31, 1997, as amended by Form 10-K/A filed on April 27, 1998;
 
          (b)  The Company's Quarterly Report on Form 10-Q for the quarter ended
     March 31, 1998;
 
          (c)  The Company's Current Report on Form 8-K filed on March 18, 1998,
     as amended by Form 8-K/A filed on April 10, 1998;
 
          (d)  The Company's Current Report on Form 8-K filed on June 18, 1998;
 
          (e)  The Company's Current Report on Form 8-K filed on July 15, 1998;
     and
 
          (f)  The Company's Registration Statement on Form 8-C relating to the
     Company's Common Stock and its Registration Statement on Form 8-A relating
     to the Company's Preferred Stock Purchase Rights, each as amended to date.
 
     All reports and other documents filed by the Company with the Commission
pursuant to Sections 13(a), 13(c), 14 and 15(d) of the Securities Exchange Act
of 1934, as amended, after the date of this Registration Statement and prior to
the termination of the offering of securities made hereby shall be deemed to be
incorporated by reference herein and to be a part hereof from the respective
dates of filing of such reports and other documents, other than the portions of
such documents which by statute, by designation in such documents or otherwise
are not required to be filed with the Commission or are not required to be
incorporated herein by reference. Any statement contained herein or in a
document incorporated or deemed to be incorporated by reference herein shall be
deemed to be modified or superseded for all purposes to the extent that a
statement contained in any other subsequently filed document that is also
incorporated or deemed to be incorporated by reference herein modifies or
supersedes such statement. Any such statement so modified or superseded shall
not be deemed, except as so modified or superseded, to constitute a part of this
Registration Statement.
 
ITEM 4. DESCRIPTION OF SECURITIES.
 
     Not applicable.
 
ITEM 5. INTERESTS OF NAMED EXPERTS AND COUNSEL.
 
     Not applicable.
 
ITEM 6. INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     The Louisiana Business Corporation Law ("LBCL") generally gives a
corporation the power to indemnify any of its directors or officers against
certain expenses, judgments, fines and amounts paid in
 
                                        2
3
 
settlement in connection with certain actions, suits or proceedings, provided
generally that such person acted in good faith and in a manner he reasonably
believed to be in or not opposed to the interests of the corporation and, with
respect to any criminal action or proceeding, had no reasonable cause to believe
his conduct was unlawful. In the case of an action by, or in the right of, the
corporation, the corporation may indemnify such person against expenses,
including attorneys' fees and amounts paid in settlement not exceeding, in the
judgment of the board of directors, the estimated expense of litigating the
action to conclusion, actually and reasonably incurred in connection with the
defense or settlement of such action, and no indemnification shall be made in
respect of any claim, issue, or matter as to which such person shall have been
adjudged by a court of competent jurisdiction, after exhaustion of all appeals
therefrom, to be liable for willful or intentional misconduct in the performance
of his duty to the corporation, unless, and only to the extent that the court
shall determine upon application that, despite the adjudication of liability but
in view of all the circumstances of the case, he is fairly and reasonably
entitled to indemnity for such expenses which the court shall deem proper.
 
     Indemnification provided pursuant to the foregoing provisions is not, under
the LBCL, deemed exclusive of any other rights to which the person indemnified
is entitled under any bylaw, agreement, authorization of shareholders or
directors; however, no such other indemnification measure shall permit
indemnification of any person for the results of such person's willful or
intentional misconduct. In addition, the LBCL contains provisions to the general
effect that any director shall in the performance of his duties be fully
protected in relying in good faith upon the records of the corporation and upon
such information, opinions, reports or statements presented to the corporation,
the board of directors, or any committee thereof by any of the corporation's
officers or employees, or by any committee of the board of directors, or by any
counsel, appraiser, engineer (including a petroleum reservoir engineer), or
independent or certified public accountant selected by the board of directors or
any committee thereof with reasonable care, or by any other person as to matters
the director reasonably believes are within such other person's professional or
expert competence and which person is selected by the board of directors or any
committee thereof with reasonable care. A director shall not be liable for the
commission of a prohibited act if his dissent was either noted in the minutes of
the meetings or filed promptly thereafter in the registered office of the
corporation.
 
     As permitted under Section 24(C)(4) of the LBCL, Article XIII of the
Restated Articles of Incorporation of the Company eliminates the personal
liability of any director or officer to the Company or its shareholders for
monetary damages for breach of fiduciary duty in such capacity, except for (i)
any breach of the duty of loyalty to the Company or its shareholders; (ii) acts
or omissions not in good faith or involving intentional misconduct or a knowing
violation of law; (iii) unlawful payment of dividends or unlawful stock purchase
or redemption; or (iv) any transaction from which the director or officer
derived an improper personal benefit.
 
     Article VI, Section 6 of the Company's Bylaws contemplates that the Company
shall indemnify its directors and officers to the maximum extent permitted by
Louisiana law.
 
     In addition, the Company has purchased a liability insurance policy under
which its directors and officers are indemnified against certain losses arising
from certain claims that may be made against them by reason of their serving in
such capacity.
 
ITEM 7. EXEMPTION FROM REGISTRATION CLAIMED.
 
     Not applicable.
 
                                        3
4
 
ITEM 8. EXHIBITS.
EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
---------------
 
* Incorporated by reference
 
ITEM 9. UNDERTAKINGS.
 
     (a) The undersigned registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this registration statement:
 
             (i) To include any prospectus required by section 10(a)(3) of the
        Securities Act of 1933 (the "Securities Act");
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of the registration statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in the registration statement;
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in the registration statement
        or any material change to such information in the registration
        statement;
 
     Provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) above shall not
     apply if the information required to be included in a post-effective
     amendment by those paragraphs is contained in periodic reports filed with
     or furnished to the Commission by the registrant pursuant to Section 13 or
     Section 15(d) of the Securities Exchange Act of 1934 (the "Exchange Act")
     that are incorporated by reference in this Registration Statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act, each such post-effective amendment shall be deemed to be a
     new registration statement relating to the securities offered therein, and
     the offering of such securities at that time shall be deemed to be the
     initial bona fide offering thereof.
 
                                        4
5
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
     (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act, each filing of the
registrant's annual report pursuant to section 13(a) or section 15(d) of the
Exchange Act that is incorporated by reference in the registration statement
shall be deemed to be a new registration statement relating to the securities
offered therein, and the offering of such securities at that time shall be
deemed to be the initial bona fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act may be permitted to directors, officers and controlling persons of the
registrant pursuant to the foregoing provisions, or otherwise, the registrant
has been advised that in the opinion of the Securities and Exchange Commission
such indemnification is against public policy as expressed in the Securities Act
and is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment by the registrant of expenses
incurred or paid by a director, officer or controlling person of the registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification by it is against public
policy as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
                                        5
6
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, the registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Houston, State of Texas, on the 17th day of July,
1998.
 
                                            SOUTHDOWN, INC.
 
                                            By:    /s/ CLARENCE C. COMER
                                              ----------------------------------
                                                      Clarence C. Comer
                                                President and Chief Executive
                                                            Officer
 
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities and on the dates indicated.
SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
/s/ CLARENCE C. COMER                   President and Chief Executive         July 17, 1998
-----------------------------------------------------     Officer and Director (Principal
                  Clarence C. Comer                       Executive Officer)
 
                 /s/ DENNIS M. THIES                    Executive Vice President --           July 17, 1998
-----------------------------------------------------     Finance and Chief Financial
                   Dennis M. Thies                        Officer (Principal Financial
                                                          Officer)
 
                /s/ ALLAN B. KORSAKOV                   Vice President and Corporate          July 17, 1998
-----------------------------------------------------     Controller (Principal Accounting
                  Allan B. Korsakov                       Officer)
 
                   /s/ R. S. EVANS                      Director                              July 17, 1998
-----------------------------------------------------
                     R. S. Evans
 
              /s/ KILLIAN L. HUGER, JR.                 Director                              July 17, 1998
-----------------------------------------------------
                Killian L. Huger, Jr.
 
                /s/ ROBERT G. POTTER                    Director                              July 17, 1998
-----------------------------------------------------
                  Robert G. Potter
 
                  /s/ FRANK J. RYAN                     Director                              July 17, 1998
-----------------------------------------------------
                    Frank J. Ryan
 
                 /s/ WHITSON SADLER                     Director                              July 17, 1998
-----------------------------------------------------
                   Whitson Sadler
 
                /s/ ROBERT J. SLATER                    Director                              July 17, 1998
-----------------------------------------------------
                  Robert J. Slater
6
7
SIGNATURE                                       TITLE                        DATE
                      ---------                                       -----                        ----
/s/ DAVID J. TIPPECONNIC                  Director                              July 17, 1998
-----------------------------------------------------
                David J. Tippeconnic
 
                /s/ J. BRUCE TOMPKINS                   Director                              July 17, 1998
-----------------------------------------------------
                  J. Bruce Tompkins
 
              /s/ GEORGE E. UDING, JR.                  Director                              July 17, 1998
-----------------------------------------------------
                George E. Uding, Jr.
 
               /s/ V. H. VAN HORN, III                  Director                              July 17, 1998
-----------------------------------------------------
                 V. H. Van Horn, III
 
               /s/ STEVEN B. WOLITZER                   Director                              July 17, 1998
-----------------------------------------------------
                 Steven B. Wolitzer
7
8
 
                                 EXHIBIT INDEX
EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
3.1            -- Restated Articles of Incorporation of the Registrant, as
                            amended through July 17, 1998.
          3.2            -- Bylaws of the Registrant, amended as of July 1, 1998.
          4.1*           -- 1989 Stock Option Plan of Registrant, as
                            amended -- incorporated by reference from Exhibit 10.2 to
                            the Registrant's Registration Statement on Form S-4
                            (Registration No. 333-49161).
          4.2*           -- Medusa Corporation 1991 Long-Term Incentive
                            Plan -- incorporated by reference from Exhibit 4.3 to
                            Medusa Corporation's Registration Statement on Form S-8
                            (Registration No. 33-45182) filed with the Commission on
                            February 20, 1996.
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            regarding the legality of the shares of Common Stock
                            covered by this Registration Statement.
         15              -- Letter of Deloitte & Touche LLP regarding unaudited
                            interim financial information.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Weiss Walmsley & Casteix, L.L.P.
                            (included in their opinion filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
---------------
 
* Incorporated by reference
 
                                        8