Magnesium alloys exhibits strong anisotropy due to HCP lattice structure and texture, which limits its application in energy-saving lightweight structures. This pronounced anisotropy cannot be captured by only classical isotropic, kinematic or mixed hardening due to the constant shape evolution of yield surfaces during plastic deformation. Therefore, the shape evolution of yield surface, known as distortional hardening is the main approach to characterize the anisotropic behaviour. Moreover, stress state is changing during forming process such as deep drawing, i.e., the loading path effect during plastic deformation must be taken into account. Thus, focusing on loading path dependent shape evolution of yield surfaces for AZ31 Mg alloy, experimental investigation on the evolution of anisotropy is performed, moreover, a constitutive model with distortional hardening is proposed based on elasto-plasticity theory at finite strain. Thermodynamical consistency is proved. The anisotropic mechanical behaviour of AZ31 Mg alloy is demonstrated after model parameters identification.