Critical currents of NbTi and Nb3Sn multifilamentary wires have been studied in magnetic fields to 9 T as a function of mechanical load applied at 4 K. Degradation of the critical current in NbTi is limited to about 30% with the effect becoming large only at strains above ∼ 1%. The change in critical current with strain is much larger in Nb3Sn, commencing at strains of 0.1 to 0.3%. For both superconductors, the first 20 to 30% decrease in critical current is almost totally reversible. A number of possible explanations of the observed degradation are considered, including filament breakage, heat generation by mechanical creep, degradation of the stabilizing matrix, and defect formation in the superconductor itself. Results of experiments to test the source of degradation are reported. Evidence for microcrack damage in the Nb3Sn reaction layer has been found and it is suggested that defect size variations on the order of a coherence length (∼ 5 nm) can account for the reversibility of the degradation as well as low-strain enhancement effects.