Using a sensitive microprofilometer, the onset of yielding in the anvils of a supported opposed anvil device can readily be determined. If the pressure at which yielding occurs is measured, the yield stress of the anvil material can be obtained. This is illustrated for 3% cobalt cemented tungsten carbide. The reverse is also true and can be used as the basis for obtaining the transition pressures of a material that transforms to a conducting phase at a pressure near which yielding of the anvil material commences. This is illustrated for the gallium phosphide transition which is found to be near 18 GPa based on the commencement of yielding in boron carbide anvils. Moreover, the yield stress or Knoop hardness can be used as the basis for obtaining the ultimate attainable pressures in supported opposed anvil devices. Based on the measured yield stress of a maraging steel, and the experimental observation that the bismuth transition is near or at the ultimate attainable pressure of this steel in a supported opposed anvil device, the III–V transition is found to be near 7.7 GPa. Based on the Knoop hardness and the previously mentioned observation, this transition is found to be near 7.5 GPa. Based on the measured yield stress of a 3% cobalt cemented tungsten carbide anvil, the ultimate pressure attainable in a supported opposed anvil device is found to be about 18 GPa and in any case less than 19 GPa. Inasmuch as the gallium phosphide transition occurs near the limit of the ultimate attainable pressure with such tungsten carbide pistons, the transition pressure of gallium phosphide to a conducting phase under the stress state present there is near 18 GPa. Based on the ultimate attainable pressure in boron carbide pistons the completion of the transition of sulfur to a conducting phase is found to be less than 33 GPa. The yielding of supported opposed diamond anvils with dislocation densities of ∼5×104/cm2or more is expected to be in the neighborhood of 50 GPa. The onset of this yielding could be used as the basis for determining approximately the transition pressure of silicon carbide to a conducting phase at an estimated value of 64 GPa.