Recently, the application of magnesium alloy to automobile and electric parts have been increased because of its high specific strength, excellent machinability, high electrical and thermal conductivity. The efforts of automobile industry to reduce fuel consumption by using lightweight structural materials have accelerated the deep drawing technology of magnesium alloy sheet. In the present study, the basic study to fabricate an automotive compressor case have been carried out. Critical damage values for a ductile fracture criterion were determined from uniaxial tensile tests and FE simulations, and then they were expressed as the function of strain rate and temperature. The proposed methodology was applied to design the deep drawing process for fabrication of Mg alloy automotive compressor case without any defect. Based on the plastic deformation histories obtained from FE analysis of the non-isothermal deep drawing process and the critical damage value curves, the initiation time and location of fracture were predicted. The results were verified with experiments.