Magnesium alloys have been widely used for many structural components of automobiles and aircraft because of high specific strength and good cast-ability in spite of hexagonal closed-packed crystal structure of pure magnesium. In this study, it is studied about the forming characteristics of press forging of AZ31 magnesium alloy by MSC/MARC in case of material having one boss and MSC/Supeiforge in case of material having multi-boss with heat transfer analysis during deformation at elevated temperature. For these results it is simulated about temperature distribution, strain distribution, and stress distribution of AZ31 Magnesium alloy. During the press forging, foot regions of bosses showed greater temperature rise than other areas of AZ31 sheet. Finally the plastic strain of AZ31 sheet did not remarkably vary with increasing temperature from 373 to 473K, while it significantly increased as the forming temperature increased from 473 to 573K, which is related with the change in micro-structures, such as dynamic re-crystallization occurring during the deformation process.