Mesa Offshore Trust (MOSH) 8-K Mesa Offshore Trust Announces No Trust Income for March 2006

Exhibit 99.1

Mesa-Offshore-Trust

Mesa Offshore Trust Announces No Trust Income for March 2006

MESA OFFSHORE TRUST

JPMorgan Chase Bank, N.A., Trustee	NEWS
	RELEASE

For Immediate Release

Austin, Texas March 21, 2006 - Mesa Offshore Trust (OTC symbol-MOSH) announced that there will be no Trust income distribution for the month of March 2006 for Unitholders of record on March 31, 2006.

Royalty income will total approximately $10,000 and Trust expenditures will be approximately $98,000. Trust expenditures in excess of royalty income received will reduce the Trust’s reserve for Trust expenses. As of February 28, 2006 the reserve for Trust expenses, excluding interest receivable, was approximately $1,580,000.

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

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700 Lavaca     Austin, TX 78701