In this research, design optimization process of axisymmetric dies for extrusion of metals is proposed. The objective function can be flow speed, stress, strain, energy, applied force, ect. Two objective functions are considered in this research; standard deviation of strain rate and rated energy consumption during extrusion process that should be minimized. A coupled numerical approach of finite element analysis in Eulerian system and an optimization technique is utilized to determine optimum die profile. This process yields more uniform strain rate distribution as possible or minimum energy concumption in the deforming region. Extrusion die profiles are defined by Bezier curves and FPS (Flexible Polyhedron Search) method is used as optimization technique. The Bezier curves are capable to produce all kinds of die profiles for a given extrusion ratio and initial radius. The results of optimum die profiles are compared with the results of non-optimum dies (conical dies). Results show that for the case of controlling strain rate in work piece, the strain values are less than that of the non-optimum conical die. In addition, the strain rate distribution of the optimum die is more uniform. In the case of minimizing energy consumption rate, results show that for the die with constant length or variable length with low friction, the die profile tends to stream line. In the die with variable length and high friction, the effect of friction is more visible and the die tends towards lower lengths. Finilly, results of this research are compared with the analytical results and good agreement has been seen. Key words Extrusion, Finite elment, Optimization, Bezier curves, Constant stran rate