Exhibit 2

Atwood Oceanics, Inc.

Lock-Up Agreement

October 5, 2004

Goldman, Sachs & Co.
Credit Suisse First Boston LLC
c/o Goldman, Sachs & Co.
85 Broad Street
New York, NY 10004

          Re: Atwood Oceanics, Inc. — Lock-Up Agreement

Ladies and Gentlemen:

     The undersigned understands that you, as representatives (the "Representatives”), propose to enter into an Underwriting Agreement on behalf of the several Underwriters named in Schedule I to such agreement (collectively, the “Underwriters”), with Atwood Oceanics, Inc., a Texas corporation (the “Company”), providing for a public offering of the Common Stock of the Company (the “Shares”) pursuant to a Registration Statement on Form S-3 filed with the Securities and Exchange Commission (the “SEC”).

     In consideration of the agreement by the Underwriters to offer and sell the Shares, and of other good and valuable consideration the receipt and sufficiency of which is hereby acknowledged, the undersigned agrees that, during the period beginning from the date hereof and continuing to and including the date 180 days after the date of the final Prospectus covering the public offering of the Shares, the undersigned will not offer, sell, contract to sell, pledge, grant any option to purchase, make any short sale or otherwise dispose of any shares of Common Stock of the Company, or any options or warrants to purchase any shares of Common Stock of the Company, or any securities convertible into, exchangeable for or that represent the right to receive shares of Common Stock of the Company, whether now owned or hereinafter acquired, owned directly by the undersigned (including holding as a custodian) or with respect to which the undersigned has beneficial ownership within the rules and regulations of the SEC (collectively the “Undersigned’s Shares”).

     The foregoing restriction is expressly agreed to preclude the undersigned from engaging in any hedging or other transaction which is designed to or which reasonably could be expected to lead to or result in a sale or disposition of the Undersigned’s Shares even if such Shares would be disposed of by someone other than the undersigned. Such prohibited hedging or other transactions would include without limitation any short sale or any purchase, sale or grant of any right (including without limitation any put or call option) with respect to any of the Undersigned’s Shares or with respect to any security that includes, relates to, or derives any significant part of its value from such Shares.

     Notwithstanding the foregoing, the undersigned may transfer the Undersigned’s Shares (i) as a bona fide gift or gifts, provided that the donee or donees thereof agree to be bound in writing by the restrictions set forth herein, (ii) to any trust for the direct or indirect benefit of the undersigned or the immediate family of the undersigned, provided that the trustee of the trust agrees to be bound in writing by the restrictions set forth herein, and provided further that any such transfer shall not involve a disposition for value, or (iii) with the prior written consent of Goldman, Sachs & Co. on behalf of the Underwriters. For purposes of this Lock-Up Agreement, “immediate family” shall mean any relationship by blood, marriage or adoption, not more remote than first cousin. In addition, notwithstanding the foregoing, if the undersigned is a corporation, the corporation may transfer the capital stock of the Company to any wholly-owned subsidiary of such corporation; provided, however, that in any such

case, it shall be a condition to the transfer that the transferee execute an agreement stating that the transferee is receiving and holding such capital stock subject to the provisions of this Agreement and there shall be no further transfer of such capital stock except in accordance with this Agreement, and provided further that any such transfer shall not involve a disposition for value. The undersigned now has, and, except as contemplated by clause (i), (ii), or (iii) above, for the duration of this Lock-Up Agreement will have, good and marketable title to the Undersigned’s Shares, free and clear of all liens, encumbrances, and claims whatsoever. The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the Undersigned’s Shares except in compliance with the foregoing restrictions.

     The undersigned understands that the Company and the Underwriters are relying upon this Lock-Up Agreement in proceeding toward consummation of the offering. The undersigned further understands that this Lock-Up Agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors, and assigns.

Very truly yours,

Exact Name of Shareholder

Authorized Signature

Title