<PAGE>   1

         As filed with the Securities and Exchange Commission on August 24, 1998
                                                    Registration No.____________

================================================================================


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933


                              LSI LOGIC CORPORATION
             (Exact Name of Registrant as specified in its charter)

              DELAWARE                                 94-2712976
    (State or Other Jurisdiction of                 (I.R.S. Employer
    Incorporation or Organization)                Identification Number)


                               1551 MCCARTHY BLVD.
                               MILPITAS, CA 95035
                        (Address, including zip code, of
                    Registrant's Principal Executive Offices)

                       SYMBIOS LOGIC INC. 1995 STOCK PLAN
                            (FULL TITLE OF THE PLAN)

                                DAVID E. SANDERS
                         VICE PRESIDENT, GENERAL COUNSEL
                              LSI LOGIC CORPORATION
                               1551 MCCARTHY BLVD.
                               MILPITAS, CA 95035
                                 (408) 433-8000
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)


                                    COPY TO:
                             Judith M. O'Brien, Esq.
                        WILSON SONSINI GOODRICH & ROSATI
                            Professional Corporation
                               650 PAGE MILL ROAD
                           PALO ALTO, CALIFORNIA 94304
                                 (650) 493-9300

<PAGE>   2


<TABLE>
<CAPTION>
                                                       CALCULATION OF REGISTRATION FEE
====================================================================================================================
                                                                                  Proposed
                                       Amount to be     Proposed Maximum           Maximum                Amount of
       Title of Securities              Registered      Offering Price Per     Aggregate Offering       Registration
        to be Registered                   (#)               Share                  Price                    Fee
--------------------------------------------------------------------------------------------------------------------
<S>                                    <C>                <C>                     <C>                     <C>  
Common Stock of the                     2,076,118          $15.46875(1)            $32,114,950             $9,732 
Company to be issued upon                                                  
exercise of options granted
under the Symbios Logic Inc. 1995
Stock Plan
</TABLE>

----------------------------------
(1)   Estimated pursuant to Rule 457(c) under the Securities Act of 1933, as
      amended (the "Act") based on the average between the high and low price as
      reported on the New York Stock Exchange on August 20, 1998.



<PAGE>   3

                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


ITEM 3.      INFORMATION INCORPORATED BY REFERENCE.

         There are hereby incorporated by reference into this Registration
Statement the following documents and information heretofore filed with the
Securities and Exchange Commission (the "Commission") by LSI Logic Corporation
(the "Registrant"):

         1.       The Registrant's Annual Report on Form 10-K for the fiscal
                  year ended December 31, 1997, filed pursuant to Section 13(a)
                  of the Securities Exchange Act of 1934, as amended (the
                  "Exchange Act").

         2.       The Registrant's Current Report on Form 8-K, filed on August
                  21, 1998 pursuant to Section 13 of the Exchange Act.

         3.       The Registrant's Current Report on Form 8-K, filed on July 2,
                  1998 pursuant to Section 13 of the Exchange Act.

         4.       The Registrant's Quarterly Reports on Form 10-Q and Form
                  10-Q/A for the quarter ended June 30, 1998, filed pursuant to
                  Section 13 of the Exchange Act.

         5.       The Registrant's Quarterly Report on Form 10-Q for the quarter
                  ended March 29, 1998, filed pursuant to Section 13 of the
                  Exchange Act.

         6.       The Registrant's Definitive Proxy Statement dated March 24,
                  1998, in connection with the Registrant's Annual Meeting of
                  Stockholders held May 12, 1998, filed pursuant to Section 14
                  of the Exchange Act.

         7.       The description of the Registrant's Common Stock contained in
                  the Registrant's Registration Statement on Form 8-A filed on
                  August 29, 1989, pursuant to Section 12(b) of the Exchange
                  Act.


         All documents filed by the Registrant pursuant to Sections 13(a),
13(c), 14 and 15(d) of 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 in this
Registration Statement and to be part hereof from the date of filing of such
documents.

ITEM 4.      DESCRIPTION OF SECURITIES.

      Not applicable.




                                        2

<PAGE>   4



ITEM 5.      INTERESTS OF NAMED EXPERTS AND COUNSEL.

         The validity of the issuance of shares of Common Stock offered
hereunder will be passed upon for the Registrant by Wilson Sonsini Goodrich &
Rosati, P.C., Palo Alto, California.


ITEM 6.      INDEMNIFICATION OF DIRECTORS AND OFFICERS.

         Section 145 of the Delaware General Corporation Law authorizes a court
to award, or a corporation's Board of Directors to grant, indemnity to directors
and officers in terms sufficiently broad to permit such indemnification under
certain circumstances for liabilities (including reimbursement for expenses
incurred) arising under the Securities Act of 1933. Section 10 of the
Certificate of Incorporation and Article VI of the Bylaws of the Registrant
provide for indemnification of certain agents to the maximum extent permitted by
the Delaware General Corporation Law. Persons covered by these indemnification
provisions include current and former directors, officers, employees and other
agents of the Registrant, as well as persons who serve at the request of the
Registrant as directors, officers, employees or agents of another enterprise. In
addition, the Registrant has entered into indemnification agreements with its
directors and officers pursuant to which the Registrant has agreed to indemnify
such individuals and to advance expenses incurred in defending any action or
proceeding to the fullest extent permitted by Section 145 of the Delaware
General Corporation Law.


ITEM 7.      EXEMPTION FROM REGISTRATION CLAIMED.

    Not applicable.


ITEM 8.      EXHIBITS.


<TABLE>
<CAPTION>
  NUMBER                                 DOCUMENT
----------   -------------------------------------------------------------------
<S>         <C>    
    4.1      Symbios Logic Inc. 1995 Stock Plan, and forms of agreement used
             thereunder.

    5.1      Opinion of Wilson Sonsini Goodrich & Rosati, Professional
             Corporation, with respect to the legality of the securities being
             registered.

    23.1     Consent of Counsel (contained in Exhibit 5.1).

    23.2     Consent of PRICEWATERHOUSECOOPERS LLP, Independent Accountants.

    24.1     Power of Attorney (See page 5).
</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 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.

                  (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.



                                        3

<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 (and, where applicable, each filing of an employee benefit plan's
annual report pursuant to 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 Delaware General Corporation Law,
Article VI of the Bylaws of the Registrant, Section 10 of the Certificate of
Incorporation of the Registrant, the indemnification provisions described above
in Item 6, or otherwise, the Registrant has been advised that in the opinion of
the 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 hereunder, 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.

                                   SIGNATURES


                  Pursuant to the requirements of the Securities Act of 1933,
the registrant, LSI Logic Corporation, 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 Milpitas, State of
California, on August 21, 1998.

                                          LSI Logic Corporation


                                      By: /s/ R. Douglas Norby
                                          -------------------------------------
                                          R. Douglas Norby
                                          Executive Vice President, Finance and
                                          Chief Financial Officer



                                        4

<PAGE>   6

                                POWER OF ATTORNEY


         KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Wilfred J. Corrigan and R. Douglas Norby,
jointly and severally, his attorneys-in-fact, each with the power of
substitution, for him in any and all capacities, to sign any amendments to this
Registration Statement on Form S-8 and to file the same, with exhibits thereto
and other documents in connection therewith, with the Securities and Exchange
Commission, hereby ratifying and confirming all that each of said
attorneys-in-fact, or his substitute or substitutes, may do or cause to be done
by virtue hereof.

         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
----------------------------------       ------------------------------------          ---------------
<S>                                      <C>                                           <C> 
/s/ Wilfred J. Corrigan                  Chief Executive Officer and Chairman          August 21, 1998
----------------------------------       of the Board of Directors (Principal
    Wilfred J. Corrigan                  Executive Officer)

/s/ R. Douglas Norby                     Executive Vice President, Finance,            August 21, 1998
----------------------------------       Chief Financial Officer and Director 
    R. Douglas Norby                     (Principal Financial and Accounting 
                                         Officer)

/s/ T. Z. Chu                            Director                                      August 21, 1998
----------------------------------
    T. Z. Chu

/s/ Malcolm R. Currie                    Director                                      August 21, 1998
----------------------------------
    Malcolm R. Currie

/s/ James H. Keyes                       Director                                      August 21, 1998
----------------------------------
    James H. Keyes
</TABLE>



                                        5

<PAGE>   7

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

--------------------------------------------------------------------------------


                                    EXHIBITS

--------------------------------------------------------------------------------


                       Registration Statement on Form S-8

                             LSI Logic Corporation

                                August 24, 1998




<PAGE>   8



                                INDEX TO EXHIBITS


<TABLE>
<CAPTION>
  NUMBER                                 DOCUMENT
----------   -------------------------------------------------------------------
<S>         <C>    
    4.1      Symbios Logic Inc. 1995 Stock Plan, and forms of agreement used
             thereunder.

    5.1      Opinion of Wilson Sonsini Goodrich & Rosati, Professional
             Corporation, with respect to the legality of the securities being
             registered.

    23.1     Consent of Counsel (contained in Exhibit 5.1).

    23.2     Consent of PRICEWATERHOUSECOOPERS LLP, Independent Accountants.

    24.1     Power of Attorney (See page 5).


</TABLE>
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 15649}]
{"company-data": {"conformed-name": "LSI LOGIC CORP", "cik": "0000703360", "assigned-sic": "3674", "irs-number": "942712976", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-62159", "film-number": "98696891"}, "business-address": {"street1": "1551 MCCARTHY BLVD", "street2": "MS D 106", "city": "MILPITAS", "state": "CA", "zip": "95035", "phone": "4084338000"}, "mail-address": {"street1": "1551 MCCARTHY BLVD", "street2": "MS D 106", "city": "MILPITAS", "state": "CA", "zip": "95035"}}
1

         As filed with the Securities and Exchange Commission on August 24, 1998
                                                    Registration No.____________

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933

                              LSI LOGIC CORPORATION
             (Exact Name of Registrant as specified in its charter)

              DELAWARE                                 94-2712976
    (State or Other Jurisdiction of                 (I.R.S. Employer
    Incorporation or Organization)                Identification Number)

                               1551 MCCARTHY BLVD.
                               MILPITAS, CA 95035
                        (Address, including zip code, of
                    Registrant's Principal Executive Offices)

                       SYMBIOS LOGIC INC. 1995 STOCK PLAN
                            (FULL TITLE OF THE PLAN)

                                DAVID E. SANDERS
                         VICE PRESIDENT, GENERAL COUNSEL
                              LSI LOGIC CORPORATION
                               1551 MCCARTHY BLVD.
                               MILPITAS, CA 95035
                                 (408) 433-8000
            (Name, address, including zip code, and telephone number,
                   including area code, of agent for service)

                                    COPY TO:
                             Judith M. O'Brien, Esq.
                        WILSON SONSINI GOODRICH & ROSATI
                            Professional Corporation
                               650 PAGE MILL ROAD
                           PALO ALTO, CALIFORNIA 94304
                                 (650) 493-9300
2
CALCULATION OF REGISTRATION FEE
====================================================================================================================
                                                                                  Proposed
                                       Amount to be     Proposed Maximum           Maximum                Amount of
       Title of Securities              Registered      Offering Price Per     Aggregate Offering       Registration
        to be Registered                   (#)               Share                  Price                    Fee
--------------------------------------------------------------------------------------------------------------------
Common Stock of the                     2,076,118          $15.46875(1)            $32,114,950             $9,732 
Company to be issued upon                                                  
exercise of options granted
under the Symbios Logic Inc. 1995
Stock Plan
----------------------------------
(1)   Estimated pursuant to Rule 457(c) under the Securities Act of 1933, as
      amended (the "Act") based on the average between the high and low price as
      reported on the New York Stock Exchange on August 20, 1998.
3

                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.      INFORMATION INCORPORATED BY REFERENCE.

         There are hereby incorporated by reference into this Registration
Statement the following documents and information heretofore filed with the
Securities and Exchange Commission (the "Commission") by LSI Logic Corporation
(the "Registrant"):

         1.       The Registrant's Annual Report on Form 10-K for the fiscal
                  year ended December 31, 1997, filed pursuant to Section 13(a)
                  of the Securities Exchange Act of 1934, as amended (the
                  "Exchange Act").

         2.       The Registrant's Current Report on Form 8-K, filed on August
                  21, 1998 pursuant to Section 13 of the Exchange Act.

         3.       The Registrant's Current Report on Form 8-K, filed on July 2,
                  1998 pursuant to Section 13 of the Exchange Act.

         4.       The Registrant's Quarterly Reports on Form 10-Q and Form
                  10-Q/A for the quarter ended June 30, 1998, filed pursuant to
                  Section 13 of the Exchange Act.

         5.       The Registrant's Quarterly Report on Form 10-Q for the quarter
                  ended March 29, 1998, filed pursuant to Section 13 of the
                  Exchange Act.

         6.       The Registrant's Definitive Proxy Statement dated March 24,
                  1998, in connection with the Registrant's Annual Meeting of
                  Stockholders held May 12, 1998, filed pursuant to Section 14
                  of the Exchange Act.

         7.       The description of the Registrant's Common Stock contained in
                  the Registrant's Registration Statement on Form 8-A filed on
                  August 29, 1989, pursuant to Section 12(b) of the Exchange
                  Act.

         All documents filed by the Registrant pursuant to Sections 13(a),
13(c), 14 and 15(d) of 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 in this
Registration Statement and to be part hereof from the date of filing of such
documents.

ITEM 4.      DESCRIPTION OF SECURITIES.

      Not applicable.

                                        2
4

ITEM 5.      INTERESTS OF NAMED EXPERTS AND COUNSEL.

         The validity of the issuance of shares of Common Stock offered
hereunder will be passed upon for the Registrant by Wilson Sonsini Goodrich &
Rosati, P.C., Palo Alto, California.

ITEM 6.      INDEMNIFICATION OF DIRECTORS AND OFFICERS.

         Section 145 of the Delaware General Corporation Law authorizes a court
to award, or a corporation's Board of Directors to grant, indemnity to directors
and officers in terms sufficiently broad to permit such indemnification under
certain circumstances for liabilities (including reimbursement for expenses
incurred) arising under the Securities Act of 1933. Section 10 of the
Certificate of Incorporation and Article VI of the Bylaws of the Registrant
provide for indemnification of certain agents to the maximum extent permitted by
the Delaware General Corporation Law. Persons covered by these indemnification
provisions include current and former directors, officers, employees and other
agents of the Registrant, as well as persons who serve at the request of the
Registrant as directors, officers, employees or agents of another enterprise. In
addition, the Registrant has entered into indemnification agreements with its
directors and officers pursuant to which the Registrant has agreed to indemnify
such individuals and to advance expenses incurred in defending any action or
proceeding to the fullest extent permitted by Section 145 of the Delaware
General Corporation Law.

ITEM 7.      EXEMPTION FROM REGISTRATION CLAIMED.

    Not applicable.

ITEM 8.      EXHIBITS.
NUMBER                                 DOCUMENT
----------   -------------------------------------------------------------------
4.1      Symbios Logic Inc. 1995 Stock Plan, and forms of agreement used
             thereunder.

    5.1      Opinion of Wilson Sonsini Goodrich & Rosati, Professional
             Corporation, with respect to the legality of the securities being
             registered.

    23.1     Consent of Counsel (contained in Exhibit 5.1).

    23.2     Consent of PRICEWATERHOUSECOOPERS LLP, Independent Accountants.

    24.1     Power of Attorney (See page 5).
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 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.

                  (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.

                                        3
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 (and, where applicable, each filing of an employee benefit plan's
annual report pursuant to 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 Delaware General Corporation Law,
Article VI of the Bylaws of the Registrant, Section 10 of the Certificate of
Incorporation of the Registrant, the indemnification provisions described above
in Item 6, or otherwise, the Registrant has been advised that in the opinion of
the 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 hereunder, 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.

                                   SIGNATURES

                  Pursuant to the requirements of the Securities Act of 1933,
the registrant, LSI Logic Corporation, 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 Milpitas, State of
California, on August 21, 1998.

                                          LSI Logic Corporation

                                      By: /s/ R. Douglas Norby
                                          -------------------------------------
                                          R. Douglas Norby
                                          Executive Vice President, Finance and
                                          Chief Financial Officer

                                        4
6

                                POWER OF ATTORNEY

         KNOW ALL PERSONS BY THESE PRESENTS, that each person whose signature
appears below constitutes and appoints Wilfred J. Corrigan and R. Douglas Norby,
jointly and severally, his attorneys-in-fact, each with the power of
substitution, for him in any and all capacities, to sign any amendments to this
Registration Statement on Form S-8 and to file the same, with exhibits thereto
and other documents in connection therewith, with the Securities and Exchange
Commission, hereby ratifying and confirming all that each of said
attorneys-in-fact, or his substitute or substitutes, may do or cause to be done
by virtue hereof.

         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/ Wilfred J. Corrigan                  Chief Executive Officer and Chairman          August 21, 1998
----------------------------------       of the Board of Directors (Principal
    Wilfred J. Corrigan                  Executive Officer)

/s/ R. Douglas Norby                     Executive Vice President, Finance,            August 21, 1998
----------------------------------       Chief Financial Officer and Director 
    R. Douglas Norby                     (Principal Financial and Accounting 
                                         Officer)

/s/ T. Z. Chu                            Director                                      August 21, 1998
----------------------------------
    T. Z. Chu

/s/ Malcolm R. Currie                    Director                                      August 21, 1998
----------------------------------
    Malcolm R. Currie

/s/ James H. Keyes                       Director                                      August 21, 1998
----------------------------------
    James H. Keyes
5
7

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

--------------------------------------------------------------------------------

                                    EXHIBITS

--------------------------------------------------------------------------------

                       Registration Statement on Form S-8

                             LSI Logic Corporation

                                August 24, 1998
8

                                INDEX TO EXHIBITS
NUMBER                                 DOCUMENT
----------   -------------------------------------------------------------------
4.1      Symbios Logic Inc. 1995 Stock Plan, and forms of agreement used
             thereunder.

    5.1      Opinion of Wilson Sonsini Goodrich & Rosati, Professional
             Corporation, with respect to the legality of the securities being
             registered.

    23.1     Consent of Counsel (contained in Exhibit 5.1).

    23.2     Consent of PRICEWATERHOUSECOOPERS LLP, Independent Accountants.

    24.1     Power of Attorney (See page 5).