<PAGE>   1
 
      AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 20, 1999
 
                                                     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 corporation 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
                HOUSTON, TEXAS                                     77002
   (Address of Principal Executive Offices)                      (Zip Code)
</TABLE>
 
 SOUTHDOWN, INC. 1991 NONQUALIFIED STOCK OPTION PLAN FOR NON-EMPLOYEE DIRECTORS
                              (Full title of plan)
 
                               PATRICK S. BULLARD
             SENIOR 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>
--------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------------
    TITLE OF SECURITIES         AMOUNT TO BE         PROPOSED MAXIMUM         PROPOSED MAXIMUM         AMOUNT OF
      TO BE REGISTERED           REGISTERED      OFFERING PRICE PER SHARE AGGREGATE OFFERING PRICE REGISTRATION FEE
--------------------------------------------------------------------------------------------------------------------
<S>                          <C>                 <C>                      <C>                      <C>
Common Stock, $1.25 par            325,000
  value(1)..................    shares(2)(3)            $63.41(4)             $20,608,250(4)           $5,730(4)
--------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------------
</TABLE>
 
(1) Includes the Preferred Stock Purchase Rights issuable pursuant to the Rights
    Agreement dated as of March 4, 1991, between the Registrant and American
    Stock Transfer & Trust Company. 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 325,000 shares are in addition to the 400,000 shares previously
    available under the Southdown, Inc. 1991 Nonqualified Stock Option Plan for
    Non-Employee Directors which have been previously registered under the
    Securities Act of 1933, as amended (the "Securities Act") pursuant to the
    registration statements referred to in the final paragraph on this facing
    page, 343,000 of which shares have not yet been issued (although options on
    167,000 of such shares have been granted). A filing fee of $2,979.74 was
    previously paid by registrant with respect to such 343,000 shares.
 
(3) Pursuant to Rule 416 under the Securities Act, includes any additional
    shares issued pursuant to the antidilution provisions of the plan.
 
(4) The price of the Common Stock is estimated in accordance with Rule 457(c)
    and (h) solely for the purpose of calculating the registration fee by
    reference to the average of the high and low sale prices of the Common Stock
    on the New York Stock Exchange on May 19, 1999 which was $63.41 per share.
 
     THE DOCUMENTS SENT OR GIVEN TO NON-EMPLOYEE DIRECTORS IN CONNECTION WITH
THE SOUTHDOWN, INC. 1991 NONQUALIFIED STOCK OPTION PLAN FOR NON-EMPLOYEE
DIRECTORS 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 AN
AGGREGATE OF 343,000 SHARES OF COMMON STOCK REGISTERED ON FORM S-8, REGISTRATION
NO. 33-45144, WHICH BECAME EFFECTIVE ON JANUARY 17, 1992, AND ON FORM S-8,
REGISTRATION NO. 333-26592, WHICH BECAME EFFECTIVE ON MAY 5, 1997.
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
<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 non-employee directors 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, 1998;
 
          (b) The Company's Quarterly Report on Form 10-Q for the quarter ended
     March 31, 1999, as amended by Form 10-Q/A dated May 14, 1999;
 
          (c) The description of the Company's Common Stock, par value $1.25 per
     share, set forth in the Company's Registration Statement on Form 8-C
     relating to such Common Stock, and the description of the Company's
     Preferred Stock Purchase Rights set forth in the Company's Registration
     Statement on Form 8-A relating to such Preferred Stock Purchase Rights, as
     each such Registration Statement is 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 (the "Exchange Act"), after the date of this Registration
Statement and prior to the filing of a post-effective amendment which indicates
that all securities offered have been sold or which deregisters all securities
then remaining unsold 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 by 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.
 
ITEM 8. EXHIBITS
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
           5             -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps 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 statements.
</TABLE>
 
                                        3
<PAGE>   4
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
          23.1           -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Walmsley & Casteix, L.L.P.
                            (included in their opinions filed as Exhibit 5 hereto).
          23.2           -- Consent of Deloitte & Touche LLP.
          99.1           -- Southdown, Inc. 1991 Nonqualified Stock Option Plan for
                            Non-Employee Directors, as amended by Amendment dated
                            March 25, 1999.
</TABLE>
 
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;
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of this 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 this 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)
        do 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 15(d) of 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 of 1933, 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.
 
          (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 of 1933, 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 this 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 of 1933 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.
 
                                        4
<PAGE>   5
 
                                   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 20th day of May,
1999.
 
                                            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 Officer    May 20, 1999
--------------------------------------    and Director (Principal Executive
          Clarence C. Comer               Officer)
 
         /s/ DENNIS M. THIES            Executive Vice President -- Finance      May 20, 1999
--------------------------------------    and Chief Financial Officer
           Dennis M. Thies                (Principal Financial Officer)
 
          /s/ ALLAN KORSAKOV            Vice President and Corporate             May 20, 1999
--------------------------------------    Controller (Principal Accounting
            Allan Korsakov                Officer)
 
         /s/ ROBERT S. EVANS            Director                                 May 20, 1999
--------------------------------------
           Robert S. Evans
 
         /s/ ROBERT G. POTTER           Director                                 May 20, 1999
--------------------------------------
           Robert G. Potter
 
          /s/ FRANK J. RYAN             Director                                 May 20, 1999
--------------------------------------
            Frank J. Ryan
 
          /s/ WHITSON SADLER            Director                                 May 20, 1999
--------------------------------------
            Whitson Sadler
 
         /s/ ROBERT J. SLATER           Director                                 May 20, 1999
--------------------------------------
           Robert J. Slater
 
       /s/ DAVID J. TIPPECONNIC         Director                                 May 20, 1999
--------------------------------------
         David J. Tippeconnic
</TABLE>
 
                                        5
<PAGE>   6
 
<TABLE>
<CAPTION>
              SIGNATURE                                 TITLE                        DATE
              ---------                                 -----                        ----
<C>                                     <S>                                      <C>
 
        /s/ J. BRUCE TOMPKINS           Director                                 May 20, 1999
--------------------------------------
          J. Bruce Tompkins
 
       /s/ GEORGE E. UDING, JR.         Director                                 May 20, 1999
--------------------------------------
         George E. Uding, Jr.
 
       /s/ V. H. VAN HORN, III          Director                                 May 20, 1999
--------------------------------------
         V. H. Van Horn, III
 
        /s/ STEVEN B. WOLITZER          Director                                 May 20, 1999
--------------------------------------
          Steven B. Wolitzer
</TABLE>
 
                                        6
<PAGE>   7
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
      EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
<C>                      <S>
          5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps 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 statements.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Walmsley & Casteix, L.L.P.
                            (included in their opinions filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
         99.1            -- Southdown, Inc. 1991 Nonqualified Stock Option Plan for
                            Non-Employee Directors, as amended by Amendment dated
                            March 25, 1999.
</TABLE>
[{"type": "S-8", "sequence": "1", "description": "SOUTHDOWN, INC.", "secsgml_size_bytes": 23098}]
{"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": "333-78955", "film-number": "99631452"}, "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 MAY 20, 1999
 
                                                     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 corporation 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
                HOUSTON, TEXAS                                     77002
   (Address of Principal Executive Offices)                      (Zip Code)
SOUTHDOWN, INC. 1991 NONQUALIFIED STOCK OPTION PLAN FOR NON-EMPLOYEE DIRECTORS
                              (Full title of plan)
 
                               PATRICK S. BULLARD
             SENIOR 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
--------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------------
    TITLE OF SECURITIES         AMOUNT TO BE         PROPOSED MAXIMUM         PROPOSED MAXIMUM         AMOUNT OF
      TO BE REGISTERED           REGISTERED      OFFERING PRICE PER SHARE AGGREGATE OFFERING PRICE REGISTRATION FEE
--------------------------------------------------------------------------------------------------------------------
Common Stock, $1.25 par            325,000
  value(1)..................    shares(2)(3)            $63.41(4)             $20,608,250(4)           $5,730(4)
--------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------------
(1) Includes the Preferred Stock Purchase Rights issuable pursuant to the Rights
    Agreement dated as of March 4, 1991, between the Registrant and American
    Stock Transfer & Trust Company. 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 325,000 shares are in addition to the 400,000 shares previously
    available under the Southdown, Inc. 1991 Nonqualified Stock Option Plan for
    Non-Employee Directors which have been previously registered under the
    Securities Act of 1933, as amended (the "Securities Act") pursuant to the
    registration statements referred to in the final paragraph on this facing
    page, 343,000 of which shares have not yet been issued (although options on
    167,000 of such shares have been granted). A filing fee of $2,979.74 was
    previously paid by registrant with respect to such 343,000 shares.
 
(3) Pursuant to Rule 416 under the Securities Act, includes any additional
    shares issued pursuant to the antidilution provisions of the plan.
 
(4) The price of the Common Stock is estimated in accordance with Rule 457(c)
    and (h) solely for the purpose of calculating the registration fee by
    reference to the average of the high and low sale prices of the Common Stock
    on the New York Stock Exchange on May 19, 1999 which was $63.41 per share.
 
     THE DOCUMENTS SENT OR GIVEN TO NON-EMPLOYEE DIRECTORS IN CONNECTION WITH
THE SOUTHDOWN, INC. 1991 NONQUALIFIED STOCK OPTION PLAN FOR NON-EMPLOYEE
DIRECTORS 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 AN
AGGREGATE OF 343,000 SHARES OF COMMON STOCK REGISTERED ON FORM S-8, REGISTRATION
NO. 33-45144, WHICH BECAME EFFECTIVE ON JANUARY 17, 1992, AND ON FORM S-8,
REGISTRATION NO. 333-26592, WHICH BECAME EFFECTIVE ON MAY 5, 1997.
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
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 non-employee directors 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, 1998;
 
          (b) The Company's Quarterly Report on Form 10-Q for the quarter ended
     March 31, 1999, as amended by Form 10-Q/A dated May 14, 1999;
 
          (c) The description of the Company's Common Stock, par value $1.25 per
     share, set forth in the Company's Registration Statement on Form 8-C
     relating to such Common Stock, and the description of the Company's
     Preferred Stock Purchase Rights set forth in the Company's Registration
     Statement on Form 8-A relating to such Preferred Stock Purchase Rights, as
     each such Registration Statement is 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 (the "Exchange Act"), after the date of this Registration
Statement and prior to the filing of a post-effective amendment which indicates
that all securities offered have been sold or which deregisters all securities
then remaining unsold 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 by 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.
 
ITEM 8. EXHIBITS
EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
5             -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps 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 statements.
3
4
EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
23.1           -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Walmsley & Casteix, L.L.P.
                            (included in their opinions filed as Exhibit 5 hereto).
          23.2           -- Consent of Deloitte & Touche LLP.
          99.1           -- Southdown, Inc. 1991 Nonqualified Stock Option Plan for
                            Non-Employee Directors, as amended by Amendment dated
                            March 25, 1999.
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;
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of this 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 this 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)
        do 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 15(d) of 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 of 1933, 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.
 
          (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 of 1933, 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 this 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 of 1933 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.
 
                                        4
5
 
                                   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 20th day of May,
1999.
 
                                            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 Officer    May 20, 1999
--------------------------------------    and Director (Principal Executive
          Clarence C. Comer               Officer)
 
         /s/ DENNIS M. THIES            Executive Vice President -- Finance      May 20, 1999
--------------------------------------    and Chief Financial Officer
           Dennis M. Thies                (Principal Financial Officer)
 
          /s/ ALLAN KORSAKOV            Vice President and Corporate             May 20, 1999
--------------------------------------    Controller (Principal Accounting
            Allan Korsakov                Officer)
 
         /s/ ROBERT S. EVANS            Director                                 May 20, 1999
--------------------------------------
           Robert S. Evans
 
         /s/ ROBERT G. POTTER           Director                                 May 20, 1999
--------------------------------------
           Robert G. Potter
 
          /s/ FRANK J. RYAN             Director                                 May 20, 1999
--------------------------------------
            Frank J. Ryan
 
          /s/ WHITSON SADLER            Director                                 May 20, 1999
--------------------------------------
            Whitson Sadler
 
         /s/ ROBERT J. SLATER           Director                                 May 20, 1999
--------------------------------------
           Robert J. Slater
 
       /s/ DAVID J. TIPPECONNIC         Director                                 May 20, 1999
--------------------------------------
         David J. Tippeconnic
5
6
SIGNATURE                                 TITLE                        DATE
              ---------                                 -----                        ----
/s/ J. BRUCE TOMPKINS           Director                                 May 20, 1999
--------------------------------------
          J. Bruce Tompkins
 
       /s/ GEORGE E. UDING, JR.         Director                                 May 20, 1999
--------------------------------------
         George E. Uding, Jr.
 
       /s/ V. H. VAN HORN, III          Director                                 May 20, 1999
--------------------------------------
         V. H. Van Horn, III
 
        /s/ STEVEN B. WOLITZER          Director                                 May 20, 1999
--------------------------------------
          Steven B. Wolitzer
6
7
 
                                 EXHIBIT INDEX
EXHIBIT NO.                                DESCRIPTION
      -----------                                -----------
5              -- Opinions of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps 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 statements.
         23.1            -- Consents of Bracewell & Patterson, L.L.P. and Correro
                            Fishman Haygood Phelps Walmsley & Casteix, L.L.P.
                            (included in their opinions filed as Exhibit 5 hereto).
         23.2            -- Consent of Deloitte & Touche LLP.
         99.1            -- Southdown, Inc. 1991 Nonqualified Stock Option Plan for
                            Non-Employee Directors, as amended by Amendment dated
                            March 25, 1999.