Recently, the applications 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. In order to apply ductile fracture criterion to predict the forming failure, critical damage values 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 magnesium automotive compressor case without any defect. Based on the simulation and experimental results, AZ31 EL-cover part 39% lighter than ADC12 die casting EL-cover could be fabricated by warm deep drawing process.