A universal scaling relationship is developed that describes the dynamic compressive strength of brittle solids. The scaling is based on the micromechanics of the growth of cracks from populations of initial flaws, and captures the fundamental dynamics of rapidly growing and interacting cracks. A characteristic stress and a characteristic strain rate are defined in terms of material and microstructural properties. The resulting model compares well with the available experimental data for ceramics and geologic materials, and demonstrates specific scaling of strength with strain rate for compressive behavior.