Magnesium alloys are of growing research, development and commercial interest for their lightweight characteristics, notably in the automotive sector. Recent results based on experiments and simulations of beam components have shown that finite element (FE) predictions using commercial FE software may significantly overestimate the peak load and load beyond the peak load. This indicates that better deformation and failure criteria are needed for crashworthiness simulation and design of Mg alloys for the development of computer-assisted engineering (CAE) capacity for Mg alloys.In this study, yield and hardening laws for deformation simulation of Mg alloys are reviewed. An isotropic Lode angle dependent von Mises yield and flow model originally used for soil was modified by replacing shear strength with tensile or compressive flow strength for deformation simulation of Mg alloys. In this law, the yield and strain hardening criteria depend on Lode angle (θ), a parameter related to the stress state of the material, e.g. θ=0corresponds to uniaxial tension and θ=30° corresponds to pure shear. For the Lode angle to equal 0°, 30° and between 0 to 30°, the criterion for the Lode angle dependent von Mises model is equivalent to the von Mises criterion, the Tresca criterion and a criterion between the Tresca and von Mises. Comparisons of predicted deformation curves with experimental results of notch tension specimens with different notch radii, and notched and un-notched three-point bend specimens show that the Lode angle dependent von Mises law has much better prediction than the von Mises law for those materials with Lode angle dependent plastic flow, such as Mg alloy. The model may also be applied to deformation simulation of cubic alloys (such as Al alloys and steel).