1998 Nonemployee Director Stock Option Plan

EXHIBIT 10 B

NONEMPLOYEE DIRECTOR STOCK OPTION AGREEMENT

     AGREEMENT made as of the ___day of                    ,                    between Rowan Companies, Inc. a Delaware corporation (the “Company”) and                                                                                  (“Director”).

     To carry out the purposes of the Rowan Companies, Inc. Nonemployee Directors Stock Option Plan (the “Plan”), by affording Director the opportunity to purchase shares of common stock of the Company (“Stock”), and in consideration of the mutual agreements and other matters set forth herein and in the Plan, the Company and Director hereby agrees as follows:

     1. Grant of Option. The Company hereby irrevocably grants to Director the right and option (“Option”) to purchase all or any part of an aggregate of                     shares of Stock, on the terms and conditions set forth herein and in the Plan, which Plan is incorporated herein by reference as a part of this Agreement.

     2. Purchase Price. The purchase price of Stock purchased pursuant to the exercise of this Option shall be $                    per share. For all purposes of this Agreement, fair market value of Stock shall be determined in accordance with the provisions of the Plan.

     3. Exercise of Option. Subject to the earlier expiration of this Option as herein provided, this Option may be exercised, by written notice to the Company at its principal executive office addressed to the attention of its Chief Financial Officer, at any time and from time to time after the date of grant hereof, but, except as otherwise provided below, this Option shall not be exercisable for more than a percentage of the aggregate number of shares offered by this Option determined by the number of full years from the date of grant hereof to the date of such exercise, in accordance with the following schedule:

     This Option may be exercised only while Director remains a director of the Company and will terminate and cease to be exercisable upon termination of Director’s status as a director of the Company, except that:

          (a) If Director’s status as a director of the Company terminates by reason of disability (within the meaning of section 22(e)(3) of the Internal Revenue Code of 1986, as amended), this Option may be exercised in full by Director (or Director’s estate or the person who acquires this Option by will or the laws of descent and distribution or otherwise by reason of the death of Director) at any time during the earlier of the five-

year period following such termination or the expiration of the original term of this Option.

          (b) If Director’s status as a director of the Company terminates on or after his attainment of the age of 70, this Option may be exercised in full by Director (or Director’s estate or the person who acquires this Option by will or the laws of descent and distribution or otherwise by reason of the death of Director) at any time during the earlier of the five-year period following such termination or the expiration of the original term of this Option.

          (c) If Director dies while a director of the Company or within a five-year period described in (a) or (b) above, Director’s estate, or the person who acquires this Option by will or the laws of descent and distribution or otherwise by reason of the death of Director, may exercise this Option in full at any time during the earlier of the two-year period following the date of Director’s death or the expiration of the original term of this Option.

This Option shall not be exercisable in any event after the expiration of ten years from the date of grant hereof. The purchase price of shares as to which this Option is exercised shall be paid in full at the time of exercise in cash (including check, bank draft or money order payable to the order of the Company). No fraction of a share of Stock shall be issued by the Company upon exercise of an Option or accepted by the Company in payment of the purchase price thereof; rather, Director shall provide a cash payment for such amount as is necessary to effect the issuance and acceptance of only whole shares of Stock. Unless and until a certificate or certificates representing such shares shall have been issued by the Company to Director, Director (or the person permitted to exercise this Option in the event of Director’s death) shall not be or have any of the rights or privileges of a shareholder of the Company with respect to shares acquirable upon an exercise of this Option.

     4. Transfer of Option. Except as provided herein, each Option and all rights granted thereunder shall not be transferable other than by will or the laws of descent and distribution and shall be exercisable during the Director’s lifetime only by the Director or, in the case of the Director’s death or incapacity, by the Director’s guardian or legal representative. Director (hereinafter the “Initial Optionee” for purposes of this Paragraph 4) may transfer this Option (in whole or in part) subject to such conditions or limitations, if any, as the Board may impose with respect to such transfer to any of (i) the spouse, children or grandchildren (“Immediate Family Members”) of the Initial Optionee, (ii) a trust or trusts for the exclusive benefit of one or more of the Immediate Family Members and, if applicable, the Initial Optionee, (iii) a partnership or limited liability company whose only partners, shareholders or members are the Initial Optionee and/or one or more Immediate Family Members or (iv) an organization that has been determined by the Internal Revenue Service to be exempt under Section 501(c)(3) of the Code. Following any transfer by the Initial Optionee, this Option may not be transferred except back to the Initial Optionee, unless the Board approves otherwise on such terms as it shall establish in its sole discretion. A transfer of this Option must be for no consideration unless the Board otherwise agrees to a transfer for consideration. The terms and conditions of the Plan and

2

this Option Agreement shall be binding upon any transferee. Following any transfer, this Option shall continue to be subject to the same terms and conditions as were applicable immediately prior to the transfer, including, without limitation, vesting and the expiration provisions of (a), (b), and (c) of Paragraph 3 above, which shall be applied “as if” Director continued to be the holder of the Option. If transferred, this Option shall not be exercisable unless arrangements satisfactory to the Company have been made to satisfy any tax withholding obligations the Company may have with respect to the transferee’s exercise of the Option. Further, the Company shall have no obligation to provide any notices to an Option transferee of any event, term or provision with respect to the Option, including, without limitation, the early termination of the Option on account of termination of Director’s status as a director of the Company. No transfer of this Option shall be effective unless the Board receives prior written notice of the terms and conditions of any intended transfer, determines that the transfer complies with the requirements imposed hereunder with respect to Option transfers and approves the transfer. Any purported assignment, alienation, pledge, attachment, sale, transfer or encumbrance of this Option that does not satisfy the requirements set forth hereunder shall be void and unenforceable against the Company.

     5. Status of Stock. The Company intends to register for issuance under the Securities Act of 1933, as amended (the “Act”) the shares of Stock acquirable upon exercise of this Option, and to keep such registration effective throughout the period this Option is exercisable. In the absence of such effective registration or an available exemption from registration under the Act, issuance of shares of Stock acquirable upon exercise of this Option will be delayed until registration of such shares is effective or an exemption from registration under the Act is available. The Company intends to use its reasonable efforts to ensure that no such delay will occur. In the event exemption from registration under the Act is available upon an exercise of this Option., Director (or the person permitted to exercise this Option in the event of Director’s death or incapacity), if requested by the Company to do so, will execute and deliver to the Company in writing an agreement containing such provisions as the Company may require to assure compliance with applicable securities laws. The Company shall incur no liability to Director for failure to register the Stock or maintain the registration.

     Director agrees that the shares of Stock which Director may acquire by exercising this Option will not be sold or otherwise disposed of in any manner which would constitute a violation of any applicable securities laws, whether federal or state. Director also agrees (i) that the certificates representing the shares of Stock purchased under this Option may bear such legend or legends as the Company deems appropriate in order to assure compliance with applicable securities laws, (ii) that the Company may refuse to register the transfer of the shares of Stock purchased under this Option on the stock transfer records of the Company if such proposed transfer would in the opinion of counsel satisfactory to the Company constitute a violation of any applicable securities law and (iii) that the Company may give related instructions to its transfer agent, if any, to stop registration of the transfer of the shares of Stock purchased under this Option.

     6. Binding Effect. This Agreement shall be binding upon and inure to the benefit of any successors to the Company and all persons lawfully claiming under Director.

3

     7. Governing Law and Venue. This Agreement shall be governed by, and construed in accordance with, the laws of the State of Texas. The courts in Harris County, Texas shall be the exclusive venue for any disputes regarding the Plan or this Agreement.

     IN WITNESS THEREOF, the Company has caused this Agreement to be duly executed by its officer thereunto duly authorized, and Director has executed this Agreement, all as of the day and year first above written.

4