Taking stress resolution of flange deformational zone of cylindrical cup drawing as an example, the stress state parameter β was revised based on the results by the usual slab method. The original yield criteria was improved using revised value β. Through the simultaneous solution of the new yield criteria and the stress equilibrium equation, the improved solutions of radial stress and tangential stress in the flange deformational zone were obtained. The derivation process of this solution was introduced, and the improved solutions were compared with the usual results. The analysis shows that the error of radial stress by the usual slab method is small, but the error of tangential stress is relatively obvious.