Abstract: Based on Hill's yield condition and its related flow rule, the plane stress characteristics equations have been developed for the first time. By using these equations, the analysis and simulation for the deep drawing process of normal anisotropic and irregular parts have been realized. In the paper, the plane stress characteristic theory is adopted to calculate and analyse the stress distribution within the flange region and along the die opening during the deep drawing process of square boxes. Furthermore, with the application of the plane stress characteristic theory founded, the optimum design for the blank shapes and its loading conditions have also been researched in this paper.