EXHIBIT 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

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

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Atwood Oceanics, Inc. (the “Company”) on Form 10-Q for the period ended December 31, 2010, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Robert J. Saltiel, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

(1)   The Report fully complies with the requirements of Section 13(a) or 15(d) 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 results of operations of the Company for the periods presented.

Date:           February 8, 2011                                                                           /s/ ROBERT J. SALTIEL

Robert J. Saltiel

President and Chief Executive Officer