The in-plane mechanical anisotropy of magnesium alloy sheet, which significantly influences the design of the parts produced by Mg alloy sheets, is of great importance regarding its wide application. Though the stress–strain response and texture evolution have been intensively investigated, and the anisotropy of Mg alloy can be significantly substantiated by its R-value, which reveals the lateral response of a material other than the primary response. As a consequence, the conjunction of viscoplastic self-consistent model and twinning and detwinning scheme (VPSC–TDT) is employed to investigate the in-plane anisotropy of magnesium alloy AZ31B-O sheet. The loading cases include both tension and compression along different paths with respect to the processing direction of the sheet. It is revealed that the stress–strain relation, texture evolution, R-value, and involved deformation mechanisms are all loading path-dependent. The unique R-values of Mg alloys are interpreted with the aid of modeling behaviors of Mg single crystals. The results agree well with the corresponding experiments. It is found that the hexagonal close-packed (HCP) crystallographic structure, deformation twinning, and initial basal texture are responsible for the characteristic behavior of Mg alloys.