Comparing the formability with each other, extrusion and various rolling experiments were carried out to make fine-grained AZ31 Mg sheets, and uni-axial tensile tests were carried out at different strain rates and temperatures to investigate the effect of different variables. A warm deep drawing tool setup with heating elements, which were distributed under the die surface and inside the blank holder, was designed and manufactured, and deep drawing was performed. Extruded Mg alloy AZ31 sheets exhibit the best deep drawing ability when working in the temperature range 250-350°C. Extruded and rolled sheets of 0.8 mm thick were also deep drawn in the lower temperature range 105-170°C，showing good formability and reaching a Limit Drawing Ratio up to 2.6 at 170°C for rolled sheets. At last, a sheet cup 0.4 mm thick was deep drawn successfully at 170 °C.