The forming failure of AZ31 alloy sheet during deep drawing processes was predicted by the FEM and ductile fracture criteria. Uniaxial tensile tests of round-notched specimens and FE simulations were performed to calculate the critical damage values for three ductile fracture criteria. The critical damage values for each criterion were expressed as a function of strain rate at various temperatures. In order to determine the best criterion for failure prediction, Erichsen cupping test under isothermal conditions at $250^{circ}C$ were conducted. Based on the plastic deformation histories obtained from the FE analysis of the Erichsen cupping tests and the critical damage value curves, the initiation time and location of fracture were predicted under bi-axial tension deformation. The results indicate that the Cockcroft-Latham criterion had good agreement with the experimental data. In addition, the FE analysis combined with the criterion was applied to another deep drawing process using an irregular shaped blank and these additional results were verified with experimental tests.