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  Annual  Report  of  Atwood  Oceanics,  Inc.  (the
"Company")  on Form 10-K for the period ended  September 30, 2005, as filed with
the Securities  and Exchange  Commission on the date hereof (the  "Report"),  I,
John R. Irwin, Chief Executive Officer of the Company,  certify,  pursuant to 18
U.S.C.  ss.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 as of, and for the periods presented.



Date:    December 14, 2005            /S/ JOHN R. IRWIN
                                      -----------------
                                      John R. Irwin
                                      President and Chief Executive Officer