**Exhibit 31**

**CERTIFICATION**

I, Mike Ulrich, certify that:

1.     I havereviewed this quarterly report on Form 10-Q of Mesa Offshore Trust, forwhich JPMorgan Chase Bank acts as Trustee;

2.     Based onmy knowledge, this report does not contain any untrue statement of a materialfact or omit to state a material fact necessary to make the statements made, inlight of the circumstances under which such statements were made, notmisleading with respect to the period covered by this report;

3.     Based onmy knowledge, the financial statements, and other financial informationincluded in this report, fairly present in all material respects the financialcondition, distributable income and changes in trust corpus of the registrantas of, and for, the periods presented in this report;

4.     I amresponsible for establishing and maintaining disclosure controls and procedures(as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)), or for causing such controls and procedures to beestablished and maintained, for the registrant and I have:

(a)    Designed such disclosure controlsand procedures, or caused such disclosure controls and procedures to bedesigned under my supervision, to ensure that material information relating tothe registrant, including its consolidated subsidiaries, is made known to me byothers within those entities, particularly during the period in which this report is beingprepared;

(b)   Evaluated the effectiveness of theregistrant’s disclosure controls and procedures and presented in this report myconclusions about the effectiveness of the disclosure controls and proceduresas of the end of the period covered by this report based on such evaluation;and

(c)    Disclosed in this report anychange in the registrant’s internal control over financial reporting thatoccurred during the registrant’s most recent fiscal quarter (the registrant’sfourth fiscal quarter in the case of an annual report) that hasmaterially affected, or is reasonably likely to materially affect, theregistrant’s internal control over financial reporting; and

5.     I havedisclosed, based on my most recent evaluation of internal control overfinancial reporting, to the registrant’s auditors:

(a)    All significant deficiencies andmaterial weaknesses in the design or operation of internal control overfinancial reporting which are reasonably likely to adversely affect theregistrant’s ability to record, process, summarize and report financialinformation; and

(b)   Any fraud, whether or notmaterial, that involves any persons who have a significant role in theregistrant’s internal control over financial reporting.

Ingiving the foregoing certifications in paragraphs 4 and 5, I have relied to theextent I consider reasonable on information provided to me by the workinginterest owners and the managing general partner of the Mesa Offshore TrustPartnership, in which the registrant owns a 99.99% interest.
| Date November 14, 2004 | /s/ MIKE  ULRICH                                           |
|------------------------|------------------------------------------------------------|
|                   | **Mike Ulrich,**                                           |
|                   | ***Vice President and Trust  Officer*JPMorgan Chase Bank** |

 

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