By modifying Griffith's theory, a theoretical fatigue model was built to explain how the fatigue strength of a single particle changes under repeated compressions. The predictions of the model were validated by experimental results for two kinds of crystal particles: NaCl and MgO. We also performed experiments on granular particles whose properties were unknown. Here too the fatigue trends were similar to that of the model. The results show that as the compression stresses acting on the particles and the number of compressions increase, the fatigue compression strength decreases. In addition, fatigue trends we observed for the various particles demonstrate dependence on the material's properties.