Using the diamond cell, we have measured the quasi-static yield strength of polycrystalline and single-crystal MgO to 40 GPa at room temperature. In contrast to previous studies we find that the yield strength is pressure dependent, increasing from 1.1 GPa at 10 GPa to 4.0 GPa at 40 GPa for polycrystalline samples subjected to small strains. This increase is an order of magnitude larger than the change in the shear modulus over the same pressure range. At 20 GPa the critical resolved shear stress for slip on the {110} system is less than 0.2 GPa, while for {100} slip it is greater than 1.9 GPa. We infer that the {100} critical resolved shear stress strongly influences the yield stress of the random polycrystalline aggregate at high pressures, as the {110} critical shear stress is relatively small and independent of pressure. We observe a large variability in the strength of polycrystalline samples depending on the amount of strain achieved in the diamond cell. Samples subjected to large strains are weakest, and they show evidence of a preferred orientation that allows slip on the weak {110} system. ¿ American Geophysical Union 1988