The crystallographic texture of AZ31B magnesium alloy processed using equal channel angular extrusion (ECAE) was found to play an important role in the flow stress anisotropy and tension-compression (T/C) asymmetry of this alloy. In order to obtain different crystallographic textures, the AZ31B Mg alloy was ECAE processed following different conventional and hybrid ECAE routes. A visco-plastic self-consistent (VPSC) crystal plasticity model was employed to predict the texture evolution during ECAE. Despite the dynamic recrystallization taking place during the ECAE processing at 200°C and the continuous grain refinement with the number of ECAE passes, the crystallographic texture was successfully predicted up to four passes. The flow stress anisotropy and T/C asymmetry of the samples processed up to four ECAE passes, were, then compared with those processed up to one and two passes only.