The viscoplastic self-consistent (VPSC) model is used to establish a combination of different deformation mechanisms. By using this model, axial tension and compression tests of extruded AZ31 magnesium alloy at room temperature are simulated. The influence of secondary deformation mechanism (prismatic slip, pyramidal slip, and 101¯1 compression twin) on mechanical response and texture evolution is expounded. Increased activity of the prismatic slip is conducive for the improvement of flow stress in mechanical response during axial tension and for the splitting of pole densities in the {0002} pole figure during axial compression. However, increased activity of the pyramidal slip causes the basal texture to transfer to the extrusion direction in the {0002} pole figure during axial compression. The 101¯1 compression twinning has a negligible influence on the plastic deformation and mechanical response of AZ31 magnesium alloy during axial tension and compression. However, the 101¯1 compression twinning should be included in VPSC modeling to predict the texture evolution accurately.