Magnesium alloy sheets bear significant potential in replacing conventional materials such as aluminium and steels in ultra lightweight designs. High specific strength and stiffness, combined with the lowest density of all structural metals make magnesium alloy sheets candidates to face the challenges of reducing vessel weight in the transportation industry and thus, green house gas emissions. For forming components from sheet metal, deep drawing is a well established and commonly applied process. Due to the limited formability of magnesium sheets at room temperature, deep drawing processes have to be conducted at elevated temperatures. In the present study, hot deep drawing experiments on an industrial scale hydraulic press were successfully conducted. Forming was done at moderately low temperatures from 150°C to 250°C. Sheets of the magnesium alloy AZ31B (Mg-3Al-1Zn-Mn) were drawn to symmetrical cups according to Swift. For AZ31, distinct basal type textures are formed during hot rolling. The influence of texture on earing is displayed. The microstructural evolution of the material is dominated by the formation of twins and dynamic recrystallisation. By optimising the process, a drawing ratio of 2.9 was achieved for AZ31 sheet, outperforming conventional materials at ambient temperature.