High mechanical strength is essential for pressure-driven membrane separations with nanoporous single-layer graphene, but its ability to withstand high pressures remains to be demonstrated. We monitored failure of centimeter-scale single-layer graphene membranes on porous supports subjected to high pressures. Consistent with theory, the membranes were found to withstand higher pressures when placed on porous supports with smaller pore diameters, but failure occurred over a surprisingly broad range of pressures, attributed to heterogeneous susceptibility to failure at wrinkles, defects, and slack in the suspended graphene. Remarkably, nonwrinkled areas withstood pressure exceeding 100 bar at which many kinds of membrane suffer from compaction. Our study shows that single-layer graphene membranes can sustain ultrahigh pressure especially if the effect of wrinkles is isolated using supports with small pores and suggests the potential for the use of single-layer graphene in high-pressure membrane separations.