In this paper, tension tests and formability tests are performed to construct a database related to mechanical properties and the formability of the AZ31B Mg alloy sheet. A forming test with a hemi-spherical punch is conducted at varying temperatures to establish a forming limit diagram. In order to verify the applicability of the analysis using the conventional flow hardening model, a finite element analysis is performed on the hemi-spherical punch forming process and the results are compared with experimental ones. The study investigates problems involving a computational analysis that does not consider flow softening of the magnesium alloy at elevated temperatures.