The three-dimensional anisotropic and asymmetric plastic response of hexagonal close-packed (HCP) basal-textured magnesium (Mg) alloys is characterized and modeled using twin-roll cast Mg sheets as a representative material. During compression tests, plastic strain localizes strongly into macroscopic bands of twinned grains (BTGs). Within these BTGs, the transverse plastic strains exhibit pronounced anisotropy. Cyclic experiments show that fatigue crack initiation consistently occurs within the BTGs. Consequently, fatigue modeling requires numerical representation of the stress-strain states within these localized regions. Therefore, a novel multi-axial constitutive model based on was developed and implemented in the finite element method (FEM) software CalculiX. The model successfully represents anisotropic yield stresses, tension-compression asymmetry, pronounced strain localization, and anisotropy in lateral plastic strains. Simulations of unnotched and notched specimens show good agreement with experimental results. Mesh refinement studies demonstrate numerical convergence without additional regularization techniques.