**Exhibit 31**

**CERTIFICATION**

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)), for theregistrant and have:

a)     designedsuch disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under my supervision, to ensure that materialinformation relating to the registrant, including its consolidatedsubsidiaries, is made known to me by others within those entities, particularlyduring the period in which this quarterly report is being prepared;

b)     evaluatedthe effectiveness of the registrant’s disclosure controls and procedures andpresented in this report my conclusions about the effectiveness of thedisclosure controls and procedures as of the end of the period covered by thisreport based on such evaluation; and

c)     disclosedin this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of our 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)     allsignificant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely toadversely affect the registrant’s ability to record, process, summarize andreport financial information; and

b)     any fraud,whether or not material, that involves any persons who have a significant rolein the registrant’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 August 11, 2004 |       | /s/ Mike  Ulrich                                           |
|---------------------------|------------|------------------------------------------------------------|
|                      | ** ** | **Mike Ulrich,**                                           |
|                      | ** ** | ***Vice President and Trust  Officer*JPMorgan Chase Bank** |

 

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