<ARTICLE> 5
<LEGEND>
THIS SCHEDULE CONTAINS SUMMARY FINANCIAL INFORMATION EXTRACTED FROM THE MESA
ROYALTY TRUST JUNE 30, 1996, FINANCIAL STATEMENTS AND IS QUALIFIED IN ITS
ENTIRETY BY REFERENCE TO SUCH FINANCIAL STATEMENTS.
</LEGEND>
<PERIOD-TYPE>                                 6-MOS
<FISCAL-YEAR-END>                          DEC-31-1995
<PERIOD-END>                               JUN-30-1996
<CASH>                                       2,290,604
<SECURITIES>                                         0
<RECEIVABLES>                                   28,087
<ALLOWANCES>                                         0
<INVENTORY>                                          0
<CURRENT-ASSETS>                             2,318,691
<PP&E>                                      42,498,034
<DEPRECIATION>                            (24,058,356)
<TOTAL-ASSETS>                              20,758,369
<CURRENT-LIABILITIES>                        2,318,691
<BONDS>                                              0
<PREFERRED-MANDATORY>                                0
<PREFERRED>                                          0
<COMMON>                                             0
<OTHER-SE>                                  18,439,678
<TOTAL-LIABILITY-AND-EQUITY>                20,758,369
<SALES>                                      4,258,312
<TOTAL-REVENUES>                             4,308,552
<CGS>                                                0
<TOTAL-COSTS>                                        0
<OTHER-EXPENSES>                                23,230
<LOSS-PROVISION>                                     0
<INTEREST-EXPENSE>                                   0
<INCOME-PRETAX>                              4,285,322
<INCOME-TAX>                                         0
<INCOME-CONTINUING>                          4,285,322
<DISCONTINUED>                                       0
<EXTRAORDINARY>                                      0
<CHANGES>                                            0
<NET-INCOME>                                 4,285,322
<EPS-PRIMARY>                                     2.30
<EPS-DILUTED>                                     2.30