**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 suchdisclosure 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 consolidated subsidiaries,is made known to me by others within those entities, particularly during theperiod in which this report 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 thisreport any change in the registrant’s internal control over financial reportingthat occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth 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, 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 reportfinancial information; and

(b)          Any fraud, whether ornot material, that involves management or other employees who have asignificant role in the registrant’s internal control over financial reporting.

In giving the foregoingcertifications in paragraphs 4 and 5, I have relied to the extent I considerreasonable on information provided to me by the working interest owners and themanaging general partner of the Mesa Offshore Trust Partnership, in which theregistrant owns a 99.99% interest.
| Date: April 16, 2007 |       | /s/ MIKE  ULRICH                                                                    |
|---------------------------|------------|-------------------------------------------------------------------------------------|
|                      | ** ** | **Mike Ulrich,**                                                                    |
|                      | ** ** | ***Vice President***                                                                |
|                      | ** ** | **The Bank of New York Trust Company, N.A.,   as attorney-in-fact for the Trustee** |

 

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