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Because of the complex boundary conditions to be dealt with, it is a difficult task to simulate the hydrodynamic deep drawing of irregular cups. If the boundary conditions on the loading of liquid pressure onto the blank are not considered correctly, the results obtained from the FEM will differ greatly from the experimental results. In this paper a mathematical model is proposed for the liquid flow between the flange and the die when drawing a tapered rectangular cup using hydrodynamic deep drawing. The proposed model was incorporated into a commercial FEM software (LS-DYNA3D), successfully. Process parameters including die entrance radius, lubrication, blank geometry, and the control of material flow for the hydrodynamic deep drawing of a tapered rectangular cup were investigated. Based an experimental unit mounted onto a single-action hydraulic press, the hydrodynamic deep drawing process was also investigated experimentally. It was shown that the FE results matched well with the experimental results, which may suggest that the proposed method can be used to determine the main process parameters during the hydrodynamic deep drawing of irregular cups. (C) 2004 Elsevier B.V. All rights reserved.