In this study, effect of drawing speed and flange temperature on formability of cylindrical cup warm deep drawing of AZ31 magnesium alloy sheet is clarified experimentally. For the purpose, a new locally heating and cooling deep drawing apparatus is designed and developed. Magnesium alloy used is AZ31 sheet with 0.5mm thickness. Firstly, tensile properties of the AZ31 sheet under various temperatures and strain rates were determined by tensile test. The experimental results indicate that the magnesium sheet possesses enough high strain rate sensitivity of m=0.25 at 400 degrees C. Cylindrical cup tests were conducted at various flange temperatures and drawing speeds to clarify suitable forming conditions. As a result, a cylindrical cup height map can be obtained and then it is concluded that the warm deep drawability intends to increases with increasing drawing speed and flange temperature, and there exists optimum conditions on temperature and drawing speed to enhance the drawability.