Mg alloy often undergoes shear deformation during industrial processing. While its anisotropy and tension-compression asymmetry have been thoroughly studied under uniaxial loading, the understanding for shear loading is still lacking. This study employed a rolled AZ31B plate with typical basal texture to investigate the shear behaviors. Positive and negative simple shear experiments were performed at different angles in the transverse plane, whereby the visco-plastic self-consistent model was calibrated to reveal the deformation mechanisms and predict the mechanical responses at various orientations. Positive-negative shear asymmetry is present because extension twinning preferentially operates in one shear direction but is suppressed in the opposite direction. Simple shear induces multiple twin variants, thus impedes twin growth and slows the consumption of matrix, as compared to in-plane compression. For slip dominated simple shear, the interaction between loading-induced rigid body rotation and slip-induced crystal rotation produces distinct hardening behaviors, namely orthogonally asymmetric mechanical responses at complementary loading angles, which is largely absent in uniaxial loading. Finally, simulation results verify that positive-negative shear asymmetry appears only when the deviatoric normal stress on the sheet plane is non-zero. Positive-negative shear asymmetry persists except for the conditions of shear plane parallel to sheet plane, or shear direction parallel or perpendicular to rolling direction.