Texture and microstructure evolutions during deep drawing of AM31 magnesium alloys were investigated at various temperatures and deformation rates. Two different types of sheets were fabricated by twin roll strip and conventional ingot casting. They were warm-rolled down to 0.6mm and then fully-annealed for deep drawing. Drawing temperatures were 200oC to 350oC and punch rates, 30mm/min, 40mm/min, and 50mm/min. The blank size and punch diameter were 74mm and 37mm, respectively, and thus overall maximum drawing ratio was 2.0. Processing maps for deep drawing of both sheets at elevated temperatures were suggested. Initial textures showed typical basal fibers with an axisymmetric arrangement. Sheets made by ingot casting had larger grain size than those by twin roll casting. The basal fibers were evolved into other orientations during deep drawing, which contained both compression along the circumferential direction in the flange and tension along the drawing direction in the cup wall. Most evident reorientations were found in the flange. With deformation, finer grains increased. Necking and cup-failure were usually expected in the lower wall near the bottom.