The study is concerned with the theoretical and experimental investigation of the elliptical bulge test. The elliptical bulge test is analyzed by using a rigid-plastic finite element method incorporating large deformation and normal anisotropy. Thin elliptical diaphragms of mild steel are bulged for three aspect ratios. The contact problem the die round and the sheet is successfully solved by using a skew boundary condition. It is shown that the proper consideration of die radius and normal anisotropy is very significant. The relation between bulging pressure and deformation is obtained. It has been found that the pole is nearly under proportional straining during deformation. The instability criterion by maximum load condition enables the effective prediction of instability pressure. The computional results are in good agreement with experimental results and to be very useful for a better understanding of the elliptical bulge test