Measurements of the effects of static and cyclic (fatigue) transverse stress on the critical current of YBCO-coated IBAD tapes are reported at 76 K in self magnetic field. YBCO films (approx. 1 um thick) on Inconel substrates (125 um thick) with IBAD buffer layers had critical-current densities (jc) exceeding 1 MA/cm2 and n values of about 50 (where n is an index of the sharpness of the superconductor-normal transition). Under static loads of 100 Mpa, the Jc degradation was less than 5% (7% at 120 Mpa). When subjected to cyclic loading, there was less than 2& additional Jc degradation after 2000 fatigue cycles. Microscopic examination of the samples indicates that this limited Jc degradation may have arisen from longitudinal cracks forming near the edges of the sample after being subjected to these high transverse pressures. This fracture mode would indicate that longitudinal side support from high-yield substrates or epoxy impregnation of the magnet structure may provide additional tolerance against Jc degradation from transverse stress.