Abstract: The materials be yielded due to its particles separated to a critical value K0 which is effected by the factors of three-dimensional stress, loading history, external environment etc. From the fundamental physical concepts of the materials composition, the yield criterion of the maximun separate displacement (MAXSD) is put forward. The MAXSP is compared with the result of the rock true triaxial compression test and that of the concrete twin-shaft, and is compared with Mohr-Coulomb’s yield criterion to prove its reasonable and suitabile for the rock and concrete brittle materials.