<PAGE>   1
      As filed with the Securities and Exchange Commission on May 26, 1998

                                                          Registration No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                       ----------------------------------
                                    FORM S-8

                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933
                       ----------------------------------
                           COOPER CAMERON CORPORATION
             (Exact name of registrant as specified in its charter)

               Delaware                                        76-0451843
   (State or other jurisdiction of                         (I.R.S. Employer
    incorporation or organization)                        Identification No.)

  515 Post Oak Boulevard, Suite 1200
             Houston, Texas                                      77027
(Address of Principal Executive Offices)                       (Zip Code)

                 AMENDED AND RESTATED COOPER CAMERON CORPORATION
                            LONG-TERM INCENTIVE PLAN
                            (Full title of the plan)

                                 Franklin Myers
              Senior Vice President, General Counsel and Secretary
                           Cooper Cameron Corporation
                       515 Post Oak Boulevard, Suite 1200
                              Houston, Texas 77027
                     (Name and address of agent for service)

                                 (713) 513-3300
          (Telephone number, including area code, of agent for service)
                       ----------------------------------

                         CALCULATION OF REGISTRATION FEE
<TABLE>
<CAPTION>
======================================================================================
                                           Proposed        Proposed
                                           Maximum         Maximum
                              Amount       Offering        Aggregate       Amount of
Title of Securities           to be        Price Per       Offering       Registration
to be Registered (1)        Registered     Share(2)        Price(3)           Fee
<S>                        <C>              <C>          <C>              <C>        
Common Stock, par value    3,000,000(4)     $59.75       $179,250,000     $ 52,880.00
$.01 per share

======================================================================================
</TABLE>

(1)      In addition, pursuant to Rule 416(c) under the Securities Act of 1934,
         this registration statement also covers an indeterminate amount of
         interests to be offered or sold pursuant to the Long-Term Incentive
         Plan.
(2)      Estimated based on the reported New York Stock Exchange composite
         transactions closing price on May 20, 1998, which is within 5 business
         days prior to the date of filing of this registration statement.
(3)      Estimated solely for the purpose of calculating the filing fee.
(4)      Each share of Common Stock offered hereby includes one purchase right
         issuable under the Cooper Cameron Corporation Rights Plan which is
         exercisable upon the occurrence of certain specified events.
<PAGE>   2
                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE.

       The following documents, which have been filed with the Securities and
Exchange Commission (the "SEC") by Cooper Cameron Corporation ("Cooper Cameron"
or the "Company"), are incorporated herein by reference and made a part hereof:

       (a)    Registration Statement on Form S-8 of Cooper Cameron Corporation
       filed with the Securities and Exchange Commission on July 26, 1995,
       relating to the Cooper Cameron Corporation Long-Term Incentive Plan (File
       No. 33-95004).

       (b) Registration Statement on Form S-8 of Cooper Cameron Corporation
       filed with the Securities and Exchange Commission on May 12, 1997,
       relating to the Amended and Restated Cooper Cameron Corporation Long-Term
       Incentive Plan (File No. 333-26923).

       (c) Annual Report on Form 10-K for the year ended December 31, 1997.

       (d) Quarterly Report on Form 10-Q for the quarter ended March 31, 1998.

       All reports subsequently filed by the Company and the Plan pursuant to
Sections 13, 14 and 15 (d) of the Securities Exchange Act of 1934, 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 herein by reference and to be a part hereof.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

       The consolidated financial statements of Cooper Cameron incorporated by
reference in Cooper Cameron's Annual Report on Form 10-K (Form 10-K) for the
year ended December 31, 1997, have been audited by Ernst & Young LLP,
independent auditors, as set forth in their report thereon incorporated by
reference therein and incorporated herein by reference. Such financial
statements are, and audited financial statements to be included in subsequently
filed documents will be, incorporated herein in reliance upon the reports of
Ernst & Young LLP pertaining to such financial statements (to the extent covered
by consents filed with the Securities and Exchange Commission) given upon the
authority of such firm as experts in accounting and auditing.

       The opinion as to the legality of the securities registered hereunder is
being given by Franklin Myers, Senior Vice President, General Counsel and
Secretary of the Company. Mr. Myers is eligible to participate in the Cooper
Cameron Corporation Long-Term Incentive Plan.

ITEM 8.  EXHIBITS

4.1    First Amended and Restated Bylaws of Cooper Cameron Corporation, filed as
       Exhibit 3.2 to the Annual Report on Form 10-K for 1996 of Cooper Cameron
       Corporation filed with the Securities and Exchange Commission on March
       26, 1997, and incorporated herein by reference.
<PAGE>   3

4.2    Amended and Restated Certificate of Incorporation of Cooper Cameron
       Corporation, dated June 30, 1995, filed as Exhibit 4.2 to the
       Registration Statement on Form S-8 of Cooper Cameron Corporation
       (Commission File No. 33-94948), and incorporated herein by reference.

4.3    Certificate of Amendment of Amended and Restated Certificate of
       Incorporation of Cooper Cameron Corporation, dated May 19, 1998.

4.4    Amended and Restated Credit Agreement, dated as of March 20, 1997, among
       Cooper Cameron Corporation and certain of its subsidiaries and the banks
       named therein and First National Bank of Chicago, as agent, filed as
       Exhibit 10.21 to the Annual Report on Form 10-K for the fiscal year ended
       December 31, 1996, and incorporated herein by reference.

4.5    Form of First Amendment to the Amended and Restated Cooper Cameron
       Corporation Long-Term Incentive Plan .

4.6    First Amendment to Rights Agreement between Cooper Cameron Corporation
       and First Chicago Trust Company of New York, as Rights Agent, dated
       November 1, 1997, filed as Exhibit 4.2 to the Annual Report on Form 10-K
       for the fiscal year ended December 31, 1997, and incorporated herein by
       reference.

5.1    Opinion and Consent of Franklin Myers, Senior Vice President, General
       Counsel and Secretary of the Company.

23.1   Consent of Franklin Myers (contained in his opinion filed as Exhibit 5.1
       hereto.)

23.2   Consent of Independent Auditors.

<PAGE>   4
                                   SIGNATURES

       THE REGISTRANT. 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 14th day of May,
1998.

                                        COOPER CAMERON CORPORATION
                                        (Registrant)


                                        /s/ Thomas R. Hix
                                        ----------------------------------------
                                        By:  Thomas R. Hix
                                        Thomas R. Hix, Senior Vice President and
                                        Chief Financial Officer

         Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities indicated on May 14, 1998:

         Signature                                      Title

/s/ Sheldon R. Erikson                      Director, Chairman, President &
______________________________________      Chief Executive Officer (principal
Sheldon R. Erikson                          executive officer)


/s/ Thomas R. Hix                           Senior Vice President & Chief
______________________________________      Financial Officer
Thomas R. Hix                               (principal financial officer)


/s/ Joseph D. Chamberlain                   Vice President & Controller
______________________________________      (principal accounting officer)
Joseph D. Chamberlain


/s/ C. Baker Cunningham                     Director
______________________________________
C. Baker Cunningham


/s/ Grant A. Dove                           Director
______________________________________
Grant A. Dove
<PAGE>   5
/s/ Michael E. Patrick                      Director
--------------------------------------
Michael E. Patrick


/s/ David Ross                              Director
--------------------------------------
David Ross


/s/ Michael J. Sebastian                    Director
--------------------------------------
Michael Sebastian



       THE PLAN. Pursuant to the requirements of the Securities Act of 1933, the
plan has duly caused this registration statement to be signed on its behalf by
the undersigned, thereunto duly authorized, in the City of Houston and State of
Texas on the 14th day of May 1998.


                                                  COOPER CAMERON CORPORATION 
                                                  LONG-TERM INCENTIVE PLAN

                                                  ADMINISTRATIVE COMMITTEE

                                                  /s/ Thomas R. Hix
                                                  ----------------------------
                                                  By:  Thomas R. Hix, Chairman


<PAGE>   6
                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT                                                                            SEQUENTIAL
NUMBER                             DESCRIPTION                                      PAGE NO.
----------------------------------------------------------------------------------------------
<S>    <C>
4.1    First Amended and Restated Bylaws of Cooper Cameron Corporation, filed as
       Exhibit 3.2 to the Annual Report on Form 10-K for 1996 of Cooper Cameron
       Corporation filed with the Securities and Exchange Commission on March
       26, 1997, and incorporated herein by reference.

4.2    Amended and Restated Certificate of Incorporation of Cooper Cameron
       Corporation, dated June 30, 1995, filed as Exhibit 4.2 to the
       Registration Statement on Form S-8 of Cooper Cameron Corporation
       (Commission File No. 33-94948), and incorporated herein by reference.

4.3    Certificate of Amendment of Amended and Restated Certificate of
       Incorporation of Cooper Cameron Corporation, dated May 19, 1998.

4.4    Amended and Restated Credit Agreement, dated as of March 20, 1997, among
       Cooper Cameron Corporation and certain of its subsidiaries and the banks
       named therein and First National Bank of Chicago, as agent, filed as
       Exhibit 10.21 to the Annual Report on Form 10-K for the fiscal year ended
       December 31, 1996, and incorporated herein by reference.

4.5    Form of First Amendment to the Amended and Restated Cooper Cameron
       Corporation Long-Term Incentive Plan.

4.6    First Amendment to Rights Agreement between Cooper Cameron Corporation
       and First Chicago Trust Company of new York, as Rights Agent, dated
       November 1, 1997, filed as Exhibit 4.2 to the Annual Report on Form 10-K
       for the fiscal year ended December 31, 1997, and incorporated herein by
       reference.

5.1    Opinion and Consent of Franklin Myers, Senior Vice President, General
       Counsel and Secretary of the Company.

23.1   Consent of Franklin Myers (contained in his opinion filed as Exhibit 5.1
       hereto.)

23.2   Consent of Independent Auditors.
</TABLE>
[{"type": "S-8", "sequence": "1", "description": "COOPER CAMERON CORPORATION", "secsgml_size_bytes": 13101}]
{"company-data": {"conformed-name": "COOPER CAMERON CORP", "cik": "0000941548", "assigned-sic": "3533", "irs-number": "760451843", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-53545", "film-number": "98631175"}, "business-address": {"street1": "515 POST OAK BLVD", "street2": "STE 1200", "city": "HOUSTON", "state": "TX", "zip": "77027", "phone": "7135133322"}, "mail-address": {"street1": "515 POST OAK BOULEVARD", "city": "HOUSTON", "state": "TX", "zip": "77027"}}
1
      As filed with the Securities and Exchange Commission on May 26, 1998

                                                          Registration No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                       ----------------------------------
                                    FORM S-8

                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933
                       ----------------------------------
                           COOPER CAMERON CORPORATION
             (Exact name of registrant as specified in its charter)

               Delaware                                        76-0451843
   (State or other jurisdiction of                         (I.R.S. Employer
    incorporation or organization)                        Identification No.)

  515 Post Oak Boulevard, Suite 1200
             Houston, Texas                                      77027
(Address of Principal Executive Offices)                       (Zip Code)

                 AMENDED AND RESTATED COOPER CAMERON CORPORATION
                            LONG-TERM INCENTIVE PLAN
                            (Full title of the plan)

                                 Franklin Myers
              Senior Vice President, General Counsel and Secretary
                           Cooper Cameron Corporation
                       515 Post Oak Boulevard, Suite 1200
                              Houston, Texas 77027
                     (Name and address of agent for service)

                                 (713) 513-3300
          (Telephone number, including area code, of agent for service)
                       ----------------------------------

                         CALCULATION OF REGISTRATION FEE
======================================================================================
                                           Proposed        Proposed
                                           Maximum         Maximum
                              Amount       Offering        Aggregate       Amount of
Title of Securities           to be        Price Per       Offering       Registration
to be Registered (1)        Registered     Share(2)        Price(3)           Fee
Common Stock, par value    3,000,000(4)     $59.75       $179,250,000     $ 52,880.00
$.01 per share

======================================================================================
(1)      In addition, pursuant to Rule 416(c) under the Securities Act of 1934,
         this registration statement also covers an indeterminate amount of
         interests to be offered or sold pursuant to the Long-Term Incentive
         Plan.
(2)      Estimated based on the reported New York Stock Exchange composite
         transactions closing price on May 20, 1998, which is within 5 business
         days prior to the date of filing of this registration statement.
(3)      Estimated solely for the purpose of calculating the filing fee.
(4)      Each share of Common Stock offered hereby includes one purchase right
         issuable under the Cooper Cameron Corporation Rights Plan which is
         exercisable upon the occurrence of certain specified events.
2
                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

ITEM 3.  INCORPORATION OF DOCUMENTS BY REFERENCE.

       The following documents, which have been filed with the Securities and
Exchange Commission (the "SEC") by Cooper Cameron Corporation ("Cooper Cameron"
or the "Company"), are incorporated herein by reference and made a part hereof:

       (a)    Registration Statement on Form S-8 of Cooper Cameron Corporation
       filed with the Securities and Exchange Commission on July 26, 1995,
       relating to the Cooper Cameron Corporation Long-Term Incentive Plan (File
       No. 33-95004).

       (b) Registration Statement on Form S-8 of Cooper Cameron Corporation
       filed with the Securities and Exchange Commission on May 12, 1997,
       relating to the Amended and Restated Cooper Cameron Corporation Long-Term
       Incentive Plan (File No. 333-26923).

       (c) Annual Report on Form 10-K for the year ended December 31, 1997.

       (d) Quarterly Report on Form 10-Q for the quarter ended March 31, 1998.

       All reports subsequently filed by the Company and the Plan pursuant to
Sections 13, 14 and 15 (d) of the Securities Exchange Act of 1934, 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 herein by reference and to be a part hereof.

ITEM 5.  INTERESTS OF NAMED EXPERTS AND COUNSEL.

       The consolidated financial statements of Cooper Cameron incorporated by
reference in Cooper Cameron's Annual Report on Form 10-K (Form 10-K) for the
year ended December 31, 1997, have been audited by Ernst & Young LLP,
independent auditors, as set forth in their report thereon incorporated by
reference therein and incorporated herein by reference. Such financial
statements are, and audited financial statements to be included in subsequently
filed documents will be, incorporated herein in reliance upon the reports of
Ernst & Young LLP pertaining to such financial statements (to the extent covered
by consents filed with the Securities and Exchange Commission) given upon the
authority of such firm as experts in accounting and auditing.

       The opinion as to the legality of the securities registered hereunder is
being given by Franklin Myers, Senior Vice President, General Counsel and
Secretary of the Company. Mr. Myers is eligible to participate in the Cooper
Cameron Corporation Long-Term Incentive Plan.

ITEM 8.  EXHIBITS

4.1    First Amended and Restated Bylaws of Cooper Cameron Corporation, filed as
       Exhibit 3.2 to the Annual Report on Form 10-K for 1996 of Cooper Cameron
       Corporation filed with the Securities and Exchange Commission on March
       26, 1997, and incorporated herein by reference.
3

4.2    Amended and Restated Certificate of Incorporation of Cooper Cameron
       Corporation, dated June 30, 1995, filed as Exhibit 4.2 to the
       Registration Statement on Form S-8 of Cooper Cameron Corporation
       (Commission File No. 33-94948), and incorporated herein by reference.

4.3    Certificate of Amendment of Amended and Restated Certificate of
       Incorporation of Cooper Cameron Corporation, dated May 19, 1998.

4.4    Amended and Restated Credit Agreement, dated as of March 20, 1997, among
       Cooper Cameron Corporation and certain of its subsidiaries and the banks
       named therein and First National Bank of Chicago, as agent, filed as
       Exhibit 10.21 to the Annual Report on Form 10-K for the fiscal year ended
       December 31, 1996, and incorporated herein by reference.

4.5    Form of First Amendment to the Amended and Restated Cooper Cameron
       Corporation Long-Term Incentive Plan .

4.6    First Amendment to Rights Agreement between Cooper Cameron Corporation
       and First Chicago Trust Company of New York, as Rights Agent, dated
       November 1, 1997, filed as Exhibit 4.2 to the Annual Report on Form 10-K
       for the fiscal year ended December 31, 1997, and incorporated herein by
       reference.

5.1    Opinion and Consent of Franklin Myers, Senior Vice President, General
       Counsel and Secretary of the Company.

23.1   Consent of Franklin Myers (contained in his opinion filed as Exhibit 5.1
       hereto.)

23.2   Consent of Independent Auditors.
4
                                   SIGNATURES

       THE REGISTRANT. 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 14th day of May,
1998.

                                        COOPER CAMERON CORPORATION
                                        (Registrant)

                                        /s/ Thomas R. Hix
                                        ----------------------------------------
                                        By:  Thomas R. Hix
                                        Thomas R. Hix, Senior Vice President and
                                        Chief Financial Officer

         Pursuant to the requirements of the Securities Act of 1933, this
registration statement has been signed by the following persons in the
capacities indicated on May 14, 1998:

         Signature                                      Title

/s/ Sheldon R. Erikson                      Director, Chairman, President &
______________________________________      Chief Executive Officer (principal
Sheldon R. Erikson                          executive officer)

/s/ Thomas R. Hix                           Senior Vice President & Chief
______________________________________      Financial Officer
Thomas R. Hix                               (principal financial officer)

/s/ Joseph D. Chamberlain                   Vice President & Controller
______________________________________      (principal accounting officer)
Joseph D. Chamberlain

/s/ C. Baker Cunningham                     Director
______________________________________
C. Baker Cunningham

/s/ Grant A. Dove                           Director
______________________________________
Grant A. Dove
5
/s/ Michael E. Patrick                      Director
--------------------------------------
Michael E. Patrick

/s/ David Ross                              Director
--------------------------------------
David Ross

/s/ Michael J. Sebastian                    Director
--------------------------------------
Michael Sebastian

       THE PLAN. Pursuant to the requirements of the Securities Act of 1933, the
plan has duly caused this registration statement to be signed on its behalf by
the undersigned, thereunto duly authorized, in the City of Houston and State of
Texas on the 14th day of May 1998.

                                                  COOPER CAMERON CORPORATION 
                                                  LONG-TERM INCENTIVE PLAN

                                                  ADMINISTRATIVE COMMITTEE

                                                  /s/ Thomas R. Hix
                                                  ----------------------------
                                                  By:  Thomas R. Hix, Chairman
6
                                  EXHIBIT INDEX
EXHIBIT                                                                            SEQUENTIAL
NUMBER                             DESCRIPTION                                      PAGE NO.
----------------------------------------------------------------------------------------------
4.1    First Amended and Restated Bylaws of Cooper Cameron Corporation, filed as
       Exhibit 3.2 to the Annual Report on Form 10-K for 1996 of Cooper Cameron
       Corporation filed with the Securities and Exchange Commission on March
       26, 1997, and incorporated herein by reference.

4.2    Amended and Restated Certificate of Incorporation of Cooper Cameron
       Corporation, dated June 30, 1995, filed as Exhibit 4.2 to the
       Registration Statement on Form S-8 of Cooper Cameron Corporation
       (Commission File No. 33-94948), and incorporated herein by reference.

4.3    Certificate of Amendment of Amended and Restated Certificate of
       Incorporation of Cooper Cameron Corporation, dated May 19, 1998.

4.4    Amended and Restated Credit Agreement, dated as of March 20, 1997, among
       Cooper Cameron Corporation and certain of its subsidiaries and the banks
       named therein and First National Bank of Chicago, as agent, filed as
       Exhibit 10.21 to the Annual Report on Form 10-K for the fiscal year ended
       December 31, 1996, and incorporated herein by reference.

4.5    Form of First Amendment to the Amended and Restated Cooper Cameron
       Corporation Long-Term Incentive Plan.

4.6    First Amendment to Rights Agreement between Cooper Cameron Corporation
       and First Chicago Trust Company of new York, as Rights Agent, dated
       November 1, 1997, filed as Exhibit 4.2 to the Annual Report on Form 10-K
       for the fiscal year ended December 31, 1997, and incorporated herein by
       reference.

5.1    Opinion and Consent of Franklin Myers, Senior Vice President, General
       Counsel and Secretary of the Company.

23.1   Consent of Franklin Myers (contained in his opinion filed as Exhibit 5.1
       hereto.)

23.2   Consent of Independent Auditors.