EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350

Pursuant to 18 U.S.C. Section 1350, the undersigned officer of Parker Drilling
Company (the "Company") hereby certifies, to such officer's knowledge, that:

     1.   The Company's Quarterly Report on Form 10-Q for the quarter ended
          March 31, 2004 (the "Report") fully complies with the requirements of
          section 13(a) or 15(d), as applicable, of the Securities Exchange Act
          of 1934; and

     2.   The information contained in the Report fairly presents, in all
          material respects, the financial condition and result of operations of
          the Company.


Dated:  May 7, 2004


/s/ Robert L. Parker Jr.
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Robert L. Parker Jr.
President and Chief Executive Officer


The foregoing certification is being furnished solely pursuant to 18 U.S.C.
Section 1350 and is not being filed as part of the Report or as a separate
disclosure statement.