Exhibit (a)(5)(B)

Cooper Cameron Extends Tender Offer

HOUSTON, May 4, 2004 — Cooper Cameron Corporation (NYSE: CAM) has extended the expiration date of its offer to purchase for cash all of its outstanding 1.75% Convertible Senior Debentures due 2021.

The tender offer, previously scheduled to expire at 9:00 a.m., New York City time, on May 5, 2004, will now expire at 3:00 p.m., New York City time, on May 5, 2004, unless further extended.

As of 3 p.m. New York City time today, $141,455,000 in principal amount of debentures have been tendered pursuant to the offer. The company’s obligation to accept the debentures for payment is subject to the terms and conditions set forth in the Offer to Purchase dated April 6, 2004 as amended and restated.

UBS Investment Bank is acting as dealer manager for the tender offer. Georgeson Shareholder Communications Inc. is acting as information agent.

Holders of the debentures with questions regarding the tender offer may contact the Liability Management Group at UBS Investment Bank, (203) 719-4210 (collect) or (888) 722-9555 ext. 4210 (toll-free). Requests for copies of the offer to purchase and the related transmittal documents should be directed to Georgeson Shareholder Communications Inc., (212) 440-9800 (call collect) or (800) 387-8819 (toll-free).

This announcement does not constitute an offer to purchase, a solicitation of an offer to purchase or a solicitation of an offer to sell securities with respect to any debentures. The tender offer is being made solely on the terms and conditions set forth in the Offer to Purchase dated April 6, 2004, as amended and restated and the accompanying transmittal documents. For additional information regarding the tender offer, reference should be made to the Offer to Purchase and the related transmittal documents.