Mesa Offshore Trust (MOSH) 8-K Mesa Offshore Trust Announces Trust Income for February 2005

Exhibit 99.1

Mesa-Offshore-Trust

Mesa Offshore Trust Announces Trust Income for February 2005

Mesa Offshore Trust

JPMorgan Chase Bank, N.A., Trustee News
Release

For Immediate Release

Austin, Texas February 18, 2005 - Mesa Offshore Trust  (OTC symbol-MOSH)

announced that there will be no Trust income distribution for the month of February 2005 for Unitholders of record on February 28, 2005.

Royalty income totaled approximately $88,000, but Trust expenditures were approximately $34,000. The Trust will withhold the difference to recoup expenses incurred by the Trust during prior periods in which there was no royalty income and to increase the reserve for Trust expenses.

The extent of future distributions from the properties in which the Trust has an interest will continue to be dependent on normal factors associated with oil and gas operations such as oil and gas production levels, prices and associated cost, accruals for future abandonment costs, timing and extent of capital expenditures.

Contact:	Mesa Offshore Trust
	JPMorgan Chase Bank, N.A., as Trustee
	Mike Ulrich
	1(800) 852-1422
	(512) 479-2562

www.businesswire.com/cnn/mosh.htm

700 Lavaca Austin, TX 78701