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

Exhibit 99.1

Mesa-Offshore-Trust

Mesa Offshore Trust Announces No Trust Income for October 2006

MESA OFFSHORE TRUST

The Bank of New York Trust Company, N.A., Trustee

NEWS
	RELEASE

For Immediate Release

Austin, Texas October 24, 2006 - Mesa Offshore Trust (OTC symbol-MOSH) announced that there will be no Trust income distribution for the month of October 2006 for Unitholders of record on October 31, 2006.

The Trust did not receive any Royalty Income from the Working Interest Owner for the month of October 2006. The Working Interest Owner withheld $1,411,141 of proceeds and added this to the abandonment accrual. The increase in the abandonment accrual is based on revised estimates to abandon all remaining Trust blocks. Trust expenditures will be approximately $85,000. Trust expenditures in excess of royalty income received will reduce the Trust’s reserve for Trust expenses. As of September 30, 2006 the reserve for Trust expenses, excluding interest receivable, was approximately $1,065,000.

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
	The Bank of New York Trust Company, N.A., as Trustee
	Mike Ulrich
	1(800) 852-1422

www.businesswire.com/cnn/mosh.htm

221 West 6th Street Austin, TX 78701