**Exhibit 31**

**CERTIFICATION**

I, Mike Ulrich,certify that:

1.     I havereviewed this annual report on Form 10-K of Mesa Offshore Trust, forwhich JPMorgan Chase Bank, N.A., 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 be established and maintained,for the registrant and I have:

(a)          Designed such disclosurecontrols and procedures, or caused such disclosure controls and procedures tobe designed under my supervision, to ensure that material information relatingto the registrant, including its consolidated subsidiaries, is made known to meby others within those entities, particularly during the period in which thisreport is being prepared;

(b)         Evaluated theeffectiveness 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)          Disclosed in this reportany change 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 has materiallyaffected or is reasonably likely to materially affect the registrant’s internalcontrol over financial reporting; and

5.     I havedisclosed, based on my most recent evaluation, to the registrant’s auditors:

(a)          All significantdeficiencies and material weaknesses in the design or operation of internalcontrol over financial reporting, which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and reportinformation; 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: March 31, 2005 |       | /s/ MIKE  ULRICH                        |
|---------------------------|------------|-----------------------------------------|
|                      | ** ** | **Mike Ulrich,**                        |
|                      | ** ** | ***Vice President and Trust  Officer*** |
|                      | ** ** | **JPMorgan Chase Bank, N.A.**           |

 

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