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The critical current of a Nb3Al wire (RHQT process) with a rectangular cross section of 1.81 × 0.80 × mm2 has been measured at 4.2 K under transverse compressive loads at fields between 15 T and 19 T. The same wire (HE2432) was previously used for winding an insert coil at NIMS (coil #B) that generated 4.5 T in a background field of 15 T at 4.2 K. In this work the load is applied perpendicularly to the narrow side of the conductor and the corresponding stresses reach 300 MPa. The critical current stays almost constant up to 150 MPa and shows a flat maximum around 75 MPa. At 300 MPa the critical current is reduced to 93%, 90% and 88% of its stress free value at 15 T, 17 T and 19 T, respectively. This indicates a rather small field dependence and significant degradation being seen only above 200 MPa. Depending on the field, unloading from 300 MPa yields to an almost complete recovery of Ic between 94% and 97% of its initial value, respectively. These observations are compared to the behavior of a Nb3Sn bronze wire.