**EXHIBIT 31**

**CERTIFICATION**

I,Mike Ulrich, certify that:

1.     I have reviewed this quarterly report on Form 10-Q ofMesa Offshore Trust, for which JPMorgan Chase Bank, N.A. acts as Trustee;

2.     Based on my knowledge, this report does not contain any untruestatement of a material fact or omit to state a material fact necessary to makethe statements made, in light of the circumstances under which such statementswere made, not misleading with respect to the period covered by this report;

3.     Based on my knowledge, the financial statements, and otherfinancial information included in this report, fairly present in all materialrespects the financial condition, distributable income and changes in trustcorpus of the registrant as of, and for, the periods presented in this report;

4.     I am responsible for establishing and maintaining disclosurecontrols and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)), or for causing such controls and procedures to be establishedand maintained, for the registrant and I have:

a)     designed such disclosure controls and procedures, or caused suchdisclosure controls and procedures to be designed under my supervision, toensure that material information relating to the registrant, including itsconsolidated subsidiaries, is made known to me by others within those entities,particularly during the period in which this report is being prepared;

b)     evaluated the effectiveness of the registrant’s disclosurecontrols and procedures and presented in this report my conclusions about theeffectiveness of the disclosure controls and procedures as of the end of theperiod covered by this report based on such evaluation; and

c)     disclosed in this report any change in the registrant’s internalcontrol over financial reporting that occurred during the registrant’s mostrecent fiscal quarter (the registrant’s fourth fiscal quarter in the case of anannual report) that has materially affected, or is reasonably likely tomaterially affect, the registrant’s internal control over financial reporting;and

5.     I have disclosed, based on my most recent evaluation of internalcontrol over financial reporting, to the registrant’s auditors:

a)     all significant deficiencies and material weaknesses in thedesign or operation of internal control over financial reporting, which arereasonably likely to adversely affect the registrant’s ability to record,process, summarize and report financial information; and

b)     any fraud, whether or not material, that involves any personswho have a significant role in the registrant’s internal control over financialreporting.

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: May 15, 2007 | /s/ MIKE ULRICH                       |
|-------------------------|--------------------------------------------|
|                    | Mike  Ulrich                               |
|                    | *Vice President and Trust Officer*         |
|                    | The  Bank of New York Trust Company, N.A., |
|                    | as  attorney-in-fact for the Trustee       |

 

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