The yield strength of materials at high pressure has diverse applications to interpretation of static and dynamic experiments, understanding mechanical performance, and constraining the rheology of planetary interiors. 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. We have used this method to explore deformation behavior (texture development, strength, slip systems) of post-perovskite phases (MgGeO3, (Mg,Fe)SiO3) at pressures above 1 Mbar. We have also studied the behavior of a suite of strong ceramics including oxides, silicates, borides, and nitrides.