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Exhibit 99.1

Mesa-Royalty-Trust

Mesa Royalty Trust Announces Trust Income for December 2004

MESA ROYALTY TRUST
JPMorgan Chase Bank, N.A., Trustee NEWS
RELEASE

FOR IMMEDIATE RELEASE

AUSTIN, TEXAS December 21, 2004—Mesa Royalty Trust (NYSE symbol-MTR) announced the Trust income distribution for the month of December 2004. Unitholders of record on December 31, 2004 will receive distributions amounting to $698,927 or $0.375043094 per unit payable on January 31, 2005. Royalty income from the San Juan Basin Properties totaled $361,012. Royalty income from the Hugoton Properties totaled $340,724.

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

www.businesswire.com/cnn/mtr.htm

        P.O. Box 550 Austin, TX 78789

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Exhibit 99.1