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To model the yield asymmetry of magnesium alloys under cyclic tension-compression, the anisotropic directional dependency, and the symmetric behaviour under cyclic pure shear, an anisotropic hardening rule based on Prager-Ziegler hardening model is developed. The proposed model is capable of making explicit reference to shear and axial cyclic material properties in different directions. Hence, the hardening parameter accounts for yield asymmetry and directional anisotropy.The application of the model to the multi-axial loading of AZ61A is carried out. Uniaxial cyclic tension-compression and shear responses of the material is employed to calibrate the material constants in the proposed model. The model is then utilized to predict the stress hysteresis under 90o out-of-phase non-proportional multi-axial loads. Results show very good agreements with the experimental results.INTRODUCTION