1
                                                                    EXHIBIT 4h


      NUMBER                                                     SHARES
- ---------------------                                     ---------------------

- ---------------------                                     ---------------------
S

                                   [LOGO]
                            ROWAN COMPANIES, INC

    COMMON STOCK                                               COMMON STOCK 
INCORPORATED UNDER THE LAWS                                  CUSIP 779382 10 0
 OF THE STATE OF DELAWARE                  THIS CERTIFICATE IS TRANSFERABLE 
                                      IN CHICAGO, ILLINOIS OR NEW YORK, NEW YORK




    THIS CERTIFIES THAT _______________________________  IS THE OWNER OF





                                                          SEE REVERSE FOR
                                                        CERTAIN DEFINITIONS

         FULL-PAID AND NON-ASSESSABLE SHARES OF COMMON STOCK OF THE
                        PAR VALUE OF $.12 1/2 EACH OF

         ROWAN COMPANIES, INC., TRANSFERABLE ON THE BOOKS OF THE CORPORATION BY
THE HOLDER HEREOF IN PERSON OR BY DULY AUTHORIZED ATTORNEY UPON SURRENDER OF
THIS CERTIFICATE PROPERLY ENDORSED.  THIS CERTIFICATE AND THE SHARES
REPRESENTED HEREBY ARE ISSUED AND SHALL BE SUBJECT TO ALL OF THE PROVISIONS OF
THE CERTIFICATE OF INCORPORATION, AS NOW OR HEREAFTER AMENDED, TO ALL OF WHICH
THE HOLDER HEREOF BY ACCEPTANCE HEREOF ASSENTS.

         THIS CERTIFICATE IS NOT VALID UNLESS COUNTERSIGNED AND REGISTERED BY A
TRANSFER AGENT AND REGISTRAR OF THE CORPORATION.

         WITNESS THE FACSMILE SEAL OF THE CORPORATION AND THE FACSMILE
SIGNATURES OF ITS DULY AUTHORIZED OFFICERS.


DATED

          MARK H. HAY                              C. R. PALMER
           SECRETARY                                PRESIDENT



                                              COUNTERSIGNED AND REGISTERED: 
            ROWAN COMPANIES, INC.             HARRIS TRUST AND SAVINGS BANK 
            CORPORATE SEAL                    TRANSFER AGENT AND REGISTRAR  
            1947                              BY                            
            DELAWARE                                                        


(C) SECURITY-COLUMBIAN UNITED STATES BANKNOTE COMPANY           AUTHORIZED AGENT
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                                                                    EXHIBIT 4h



                             ROWAN COMPANIES, INC.

         THE CORPORATION WILL FURNISH WITHOUT CHARGE TO EACH STOCKHOLDER WHO SO
REQUESTS A STATEMENT OF THE POWERS, DESIGNATIONS, PREFERENCES AND RELATIVE,
PARTICIPATING, OPTIONAL OR OTHER SPECIAL RIGHTS OF EACH CLASS OF STOCK OR
SERIES THEREOF OF THE CORPORATION, AND THE QUALIFICATIONS, LIMITATIONS OR
RESTRICTIONS OF SUCH PREFERENCES AND/OR RIGHTS.  SUCH REQUEST MAY BE MADE TO
THE CORPORATION OR TO THE TRANSFER AGENT.

         The following abbreviations, when used in the inscription on the face
of this certificate, shall be construed as though they were written out in full
according to applicable laws or regulations:


                                           
TEN COM - as tenants in common                 UNIF GIFT MIN ACT        Custodian           
TEN ENT - as tenants by the entireties                          --------         -----------
JT TEN  - as joint tenants with right of                         (Cust)            (Minor)  
          survivorship and not as tenants                      under Uniform Gifts to Minors
          in common                                            Act 
                                                                  ---------                 
                                                                   (State)                  



   Additional abbreviations may also be used though not in the above list.

      For Value Received,__________hereby sell, assign and transfer unto

         PLEASE INSERT SOCIAL SECURITY OR OTHER
             IDENTIFYING NUMBER OF ASSIGNEE

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

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

________________________________________________________________________________
 (PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE)

________________________________________________________________________________

________________________________________________________________________________

_________________________________________________________________________ SHARES
OF THE CAPITAL STOCK REPRESENTED BY THE WITHIN CERTIFICATE, AND DO HEREBY 
IRREVOCABLY CONSTITUTE AND APPOINT

_______________________________________________________________________ ATTORNEY
TO TRANSFER THE SAID SHARES ON THE BOOKS OF THE WITHIN NAMED
CORPORATION WITH FULL POWER OF SUBSTITUTION IN THE PREMISES.

DATED_________________________________


                       _________________________________________________________
                       THE SIGNATURE TO THIS ASSIGNMENT MUST CORRESPOND WITH
                       THE NAME AS WRITTEN UPON THE FACE OF
              NOTICE:  THE CERTIFICATE IN EVERY PARTICULAR, WITHOUT ALTERATION 
                       OR ENLARGEMENT OR ANY CHANGE WHATEVER.




                 This certificate also evidences and entitles the holder hereof
to certain Rights as set forth in the Rights Agreement between Rowan Companies,
Inc. (the "Company") and Citibank, N.A. (the "Rights Agent") dated as of
February 25, 1992 (the "Rights Agreement"), the terms of which are hereby
incorporated herein by reference and a copy of which is on file at the
principal office of the Company.  Under certain circumstances, as set forth in
the Rights Agreement, such Rights may be redeemed, may expire, or may be
evidenced by separate certificates and will no longer be evidenced by this
certificate.  The Company will mail to the holder of this certificate a copy of
the Rights Agreement, as in effect on the date of mailing, without charge
promptly after receipt of a written request therefor.  Under certain
circumstances set forth in the Rights Agreement, Rights issued to, or held by,
any Person who is, was or becomes an Acquiring Person or any Affiliate or
Associate thereof (as such terms are defined in the Rights Agreement), whether
currently held by or on behalf of such Person or by any subsequent holder, may
become null and void.