In order to predict the failure of AZ31B Mg sheet at room temperature under uniaxial and biaxial loading paths, analytical expressions based on the maximum shear stress criterion in conjunction with the quadratic anisotropic yield function and plastic potential were developed. By utilizing the formulations based on the associated flow rule (AFR) and the non-associated flow rule (NAFR), different levels of material anisotropy were considered with the developed equations. Material coefficients of anisotropy were obtained from tensile and bulge tests taking into account the differential work hardening of AZ31B Mg sheet. Failure predictions were performed and compared with the experimental failure strains measured by the hemispherical dome tests at room temperature. In the failure prediction of AZ31B Mg sheet, it was found that the material anisotropy and the differential work hardening exhibited by the AZ31B Mg sheet were primary factors which have a major influence on the results of failure prediction, and the formulations based on the NAFR with the material coefficients obtained by taking into account the differential work hardening showed good accuracy by yielding failure predictions close to the experimentally measured failure strains.