Strength properties of materials under static and dynamic loading are essential quantities for characterizing mechanical behavior. Quantitative measurements of static strengths achieved in the diamond anvil cell can be made using x-ray diffraction in a radial geometry for samples under non-hydrostatic compression. Results for several metals up to 68 GPa show that the ratio of yield strength to shear modulus ranges from 0.01-0.03 and increases weakly with compression. Trends at lower pressure for Re, W, and epsilon-Fe are consistent with available data above 1 Mbar. Strong ceramics such as B6O, c-Si3N4, and TiB2 achieve yield strengths as large at 10% of the shear modulus at pressures up to similar to 70 GPa. Strengths of materials used as pressure media are quantitatively compared and evaluated.