A fracture mechanism and forming limit in cylindrical deep-drawing below 473 K was investigated for commercially rolled sheet of magnesium alloy AZ31. A small punch radius, of which the ratio to thickness was 2.5, was adopted intentionally. At room temperature, a brittle fracture under a very small punch load occurred at an early stage on the punch shoulder near the bottom. It was confirmed by stretch bending tests that the fracture was caused by bending under high tension, which deeply concerned with high yield stress and little local elongation of this material. The forming limit was dominated by this mechanism up to 453 K in semi-static drawing.