A method of determining an optimum blank shape for the non-circular deep drawing process is investigated. The rigid-plastic finite element method is introduced and the computer program code is developed. The ideal shape of a drawn cup with uniform wall height is assumed and metal flow is traced back-ward step by step to predict an initial blank shape of the ideal cup. For examples of the non-circular deep drawing products, three cases of drawn cup with quadrilateral punch shape are considered and optimum blank shapes for each case are proposed and compared with experimental results.