To investigate the deformation twinning and the plastic anisotropy of the hexagonal-close-packed（HCP） single crystal, the crystal plastic constitutive model including slip and twinning deformation was established with finite element method based on crystal plasticity theory. The model was verified by test data. Newton-Raphson iteration method was developed with the stress components directly as the basic variables of iteration. The plastic deformation behavior of single crystal AZ31 alloy was analyzed numerically under monotonic tension and compression, respectively, in four different strain paths（i.e. along 〈2110〉, 〈 0110〉, 〈0001〉 and 〈0111〉） with this model. The stress-strain curves were obtained in the above paths. The numerical calculation results show that this crystal model is feasible to predict the activity of slip/twinning system and to describe the number of active twin variants, the types of dominant twin variants and twin intersection. Due to the polar nature of mechanical twinning in inelastic deformation of the material, the plastic behavior of the single crystal material is demonstrated to be notably anisotropic and high asymmetry.
