A theory of crystal plasticity including back stress and damage evolutions has been established in this paper. The effects of strain rate on the matrix and precipitate phases of Ni-base superalloy have been analyzed using the theory. The computational result revealed that the both matrix and precipitate phases were seriously affected by strain rate. The nonuniform microcosmic stresses and plastic slips were induced by the microcosmic heterogeneity of single crystal dual phase alloy. The microcosmic plastic slips originate in matrix firstly. The heterogeneity of microcosmic stresses and plastic slips is probably the origin of the damage evolution and the nucleation of micro voids.