<PAGE>   1
         As filed with the Securities and Exchange Commission on June 29, 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)


              INDIVIDUAL ACCOUNT  RETIREMENT PLAN FOR HOURLY-PAID
                  EMPLOYEES AT THE COOPER CAMERON CORPORATION
                               MOUNT VERNON PLANT
                            (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    12,000(4)     $52.375       $628,500       $186.00
$.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 June 25, 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)    Annual Report on Form 10-K for the year ended December 31,
                     1997.

              (b)    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 (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 not eligible to participate
in the Individual Account Retirement Plan for Hourly-Paid Employees at the
Cooper Cameron Corporation Mount Vernon Plant.

ITEM 6.       INDEMNIFICATION OF DIRECTORS AND OFFICERS.

              Section 145 of the Delaware General Corporation Law permits a
corporation to indemnify any person who was or is a party or is threatened to be
made a party to any threatened, pending or completed action, suit or proceeding,
whether civil, criminal, administrative or investigative, by reason of the fact
that he is or was a director, officer, employee or agent of the corporation or
is or was serving at the request of the corporation as a director, officer,
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise against expenses (including attorneys' fees), judgments, fines
and amounts paid in settlement actually and reasonably incurred by him in
connection with such action.

              In a suit brought to obtain a judgment in the corporation's favor,
whether by the corporation itself or derivatively by a stockholder, the
corporation may only indemnify for expenses, including attorney's fees, actually
and reasonably incurred in connection with the defense or settlement of the
case, and the corporation may not indemnify for amounts paid in satisfaction of
a judgment or in settlement of the claim. In any such action, no indemnification
may be paid in respect of any claim, issue or matter as to which such persons
shall have been adjudged liable to the corporation except as otherwise approved
by the Delaware Court of Chancery or the court in which the claim was brought.
In any other type of proceeding, the indemnification may extend to judgments,
fines and amounts paid in settlement, actually and reasonably incurred in
connection with such other proceedings, as well as to expenses (including
attorneys' fees).

              The statute does not permit indemnification unless the person
seeking indemnification has acted in good faith and in a manner he reasonably
believed to be in, or not opposed to, the best interests of the corporation and,
in the case of criminal actions or proceedings, the person had no reasonable
cause to believe his conduct was unlawful. There are additional limitations
applicable to criminal actions and to actions brought by or in the name of the
corporation. The determination as to whether a person seeking indemnification
has met the required standard of conduct is to be made (i) by a majority vote of
a quorum or disinterested members of the board of directors; or (ii) by
independent legal counsel in a written opinion, if such a quorum does not exist
or if the disinterested directors so direct; or (iii) by the stockholders.

              The Certificate of Incorporation and bylaws of the Company require
the Company to indemnify the Registrant's directors and officers to the fullest
extent permitted under Delaware law, and to implement provisions pursuant to
contractual indemnity agreements the Company has entered into with its directors
and executive officers. The Certificate limits the personal liability of a
director to the Company or its stockholders to damages for breach of the
director's fiduciary duty. The Company has purchased insurance on behalf of its
directors and officers against certain liabilities that may be asserted or
incurred by such persons in their capacities as directors or officers of the
Company, or that may arise tout of their status as directors or officers of the
Company, including liabilities under the federal and state securities laws.

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.

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.
<PAGE>   3
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    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.

4.6    Individual Account Retirement Plan for Hourly-Paid Employees at the
       Cooper Cameron  Corporation Mount Vernon Plant (January 1, 1995
       Restatement).

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.

24.1   Powers of Attorney from certain members of Cooper Cameron Corporation
       Board of Directors.

24.2   Certified copy of resolutions authorizing signatures pursuant to Power
       of Attorney.

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 1993,

                  (ii)     to reflect in the prospectus any facts or events
                           arising after the effective date of the registration
                           statement (or the most recent post-effective
                           amendment thereof) which, individually or in the
                           aggregate, represent a fundamental change in the
                           information set forth in the registration statement;

                  (iii)    to include any material information with respect to
                           the plan of distribution not previously disclosed in
                           the registration statement or any material change to
                           such information in the registration statement;
                           provided, however, that the undertakings set forth in
                           paragraphs (a)(1)(i) and (a)(1)(ii) above do not
                           apply if the information required to be included in a
                           post-effective amendment by those paragraphs is
                           contained in periodic reports filed by the registrant
                           pursuant to Section 13 or Section 15(d) of the
                           Exchange Act that are incorporated by reference in
                           the 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 (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 provisions described under Item 6
above, 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, 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.

<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 29th
day of June, 1998.


                                       COOPER CAMERON CORPORATION            
                                       (Registrant)                          
                                                                             
                                                                             
                                       /s/ Franklin Myers                    
                                                                             
                                       By:                                   
                                          -----------------------------------
                                       Franklin Myers, Senior Vice President,
                                       General Counsel and Secretary         


     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 June 29, 1998:


     Signature                                    Title
     ---------                                    -----

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

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

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


/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                     


*By: /s/ Franklin Myers
    --------------------------
    Franklin Myers, Senior Vice President                  
    General Counsel and Secretary


     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 26th day of June 1998.


                                           INDIVIDUAL ACCOUNT RETIREMENT
                                           PLAN FOR HOURLY-PAID EMPLOYEES AT THE
                                           COOPER CAMERON CORPORATION MOUNT
                                           VERNON PLANT ADMINISTRATIVE COMMITTEE

                                           /s/ Thomas R. Hix
                                           -------------------------------------
                                           By: Thomas R. Hix, Chairman
<PAGE>   6
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT
NUMBER               DESCRIPTION
--------------------------------------------------------------------------------
<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    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.

4.6    Individual Account Retirement Plan for Hourly-Paid Employees at the
       Cooper Cameron Corporation Mount Vernon Plant (January 1, 1995
       restatement).

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.

24.1   Powers of  Attorney from certain members of Cooper Cameron Corporation
       Board of Directors.

24.2   Certified copy of resolutions authorizing signatures pursuant to Power
       of Attorney.
</TABLE>
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{"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": "333-58005", "film-number": "98656777"}, "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 June 29, 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)

              INDIVIDUAL ACCOUNT  RETIREMENT PLAN FOR HOURLY-PAID
                  EMPLOYEES AT THE COOPER CAMERON CORPORATION
                               MOUNT VERNON PLANT
                            (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    12,000(4)     $52.375       $628,500       $186.00
$.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 June 25, 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)    Annual Report on Form 10-K for the year ended December 31,
                     1997.

              (b)    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 (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 not eligible to participate
in the Individual Account Retirement Plan for Hourly-Paid Employees at the
Cooper Cameron Corporation Mount Vernon Plant.

ITEM 6.       INDEMNIFICATION OF DIRECTORS AND OFFICERS.

              Section 145 of the Delaware General Corporation Law permits a
corporation to indemnify any person who was or is a party or is threatened to be
made a party to any threatened, pending or completed action, suit or proceeding,
whether civil, criminal, administrative or investigative, by reason of the fact
that he is or was a director, officer, employee or agent of the corporation or
is or was serving at the request of the corporation as a director, officer,
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise against expenses (including attorneys' fees), judgments, fines
and amounts paid in settlement actually and reasonably incurred by him in
connection with such action.

              In a suit brought to obtain a judgment in the corporation's favor,
whether by the corporation itself or derivatively by a stockholder, the
corporation may only indemnify for expenses, including attorney's fees, actually
and reasonably incurred in connection with the defense or settlement of the
case, and the corporation may not indemnify for amounts paid in satisfaction of
a judgment or in settlement of the claim. In any such action, no indemnification
may be paid in respect of any claim, issue or matter as to which such persons
shall have been adjudged liable to the corporation except as otherwise approved
by the Delaware Court of Chancery or the court in which the claim was brought.
In any other type of proceeding, the indemnification may extend to judgments,
fines and amounts paid in settlement, actually and reasonably incurred in
connection with such other proceedings, as well as to expenses (including
attorneys' fees).

              The statute does not permit indemnification unless the person
seeking indemnification has acted in good faith and in a manner he reasonably
believed to be in, or not opposed to, the best interests of the corporation and,
in the case of criminal actions or proceedings, the person had no reasonable
cause to believe his conduct was unlawful. There are additional limitations
applicable to criminal actions and to actions brought by or in the name of the
corporation. The determination as to whether a person seeking indemnification
has met the required standard of conduct is to be made (i) by a majority vote of
a quorum or disinterested members of the board of directors; or (ii) by
independent legal counsel in a written opinion, if such a quorum does not exist
or if the disinterested directors so direct; or (iii) by the stockholders.

              The Certificate of Incorporation and bylaws of the Company require
the Company to indemnify the Registrant's directors and officers to the fullest
extent permitted under Delaware law, and to implement provisions pursuant to
contractual indemnity agreements the Company has entered into with its directors
and executive officers. The Certificate limits the personal liability of a
director to the Company or its stockholders to damages for breach of the
director's fiduciary duty. The Company has purchased insurance on behalf of its
directors and officers against certain liabilities that may be asserted or
incurred by such persons in their capacities as directors or officers of the
Company, or that may arise tout of their status as directors or officers of the
Company, including liabilities under the federal and state securities laws.

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.

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.
3
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    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.

4.6    Individual Account Retirement Plan for Hourly-Paid Employees at the
       Cooper Cameron  Corporation Mount Vernon Plant (January 1, 1995
       Restatement).

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.

24.1   Powers of Attorney from certain members of Cooper Cameron Corporation
       Board of Directors.

24.2   Certified copy of resolutions authorizing signatures pursuant to Power
       of Attorney.

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 1993,

                  (ii)     to reflect in the prospectus any facts or events
                           arising after the effective date of the registration
                           statement (or the most recent post-effective
                           amendment thereof) which, individually or in the
                           aggregate, represent a fundamental change in the
                           information set forth in the registration statement;

                  (iii)    to include any material information with respect to
                           the plan of distribution not previously disclosed in
                           the registration statement or any material change to
                           such information in the registration statement;
                           provided, however, that the undertakings set forth in
                           paragraphs (a)(1)(i) and (a)(1)(ii) above do not
                           apply if the information required to be included in a
                           post-effective amendment by those paragraphs is
                           contained in periodic reports filed by the registrant
                           pursuant to Section 13 or Section 15(d) of the
                           Exchange Act that are incorporated by reference in
                           the 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 (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 provisions described under Item 6
above, 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, 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
                                   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 29th
day of June, 1998.

                                       COOPER CAMERON CORPORATION            
                                       (Registrant)                          
                                                                             
                                                                             
                                       /s/ Franklin Myers                    
                                                                             
                                       By:                                   
                                          -----------------------------------
                                       Franklin Myers, Senior Vice President,
                                       General Counsel and Secretary         

     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 June 29, 1998:

     Signature                                    Title
     ---------                                    -----

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

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

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

/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                     

*By: /s/ Franklin Myers
    --------------------------
    Franklin Myers, Senior Vice President                  
    General Counsel and Secretary

     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 26th day of June 1998.

                                           INDIVIDUAL ACCOUNT RETIREMENT
                                           PLAN FOR HOURLY-PAID EMPLOYEES AT THE
                                           COOPER CAMERON CORPORATION MOUNT
                                           VERNON PLANT ADMINISTRATIVE COMMITTEE

                                           /s/ Thomas R. Hix
                                           -------------------------------------
                                           By: Thomas R. Hix, Chairman
6
                                 EXHIBIT INDEX
EXHIBIT
NUMBER               DESCRIPTION
--------------------------------------------------------------------------------
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    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.

4.6    Individual Account Retirement Plan for Hourly-Paid Employees at the
       Cooper Cameron Corporation Mount Vernon Plant (January 1, 1995
       restatement).

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.

24.1   Powers of  Attorney from certain members of Cooper Cameron Corporation
       Board of Directors.

24.2   Certified copy of resolutions authorizing signatures pursuant to Power
       of Attorney.