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 September 30, 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: November 8, 2004 /s/ Robert L. Parker Jr. - -------------------------------------- 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.