In this study, an analytical method is proposed for determination and minimization of the exit CURVATURE in extrusion dies. The stream lines are determined by using the Bezier formulation. The improved Bezier formulation is achieved by adding some parameters to the stream line equations and the non-uniform velocity field is extracted from the improved Bezier formulation. By defining the exit CURVATURE criteria, the die is optimized, according to the Bezier coefficients and eccentricity values.For verification of the proposed procedure, the exit CURVATURE of some selective dies is calculated by using Abaqus FEM Software. The FEM results show good agreement with the proposed procedure. Finally the extrusion pressure of the dies is calculated, based on the minimum energy consumption criteria, according to the upper-bound method. Then, the estimated pressures, according to the minimum CURVATURE and minimum energy criterion, are compared.