Extrusion die profile has a significant role on material flow characteristics, product microstructure, die life, and required load. Nowadays, economic requirements and effort to improve and homogenize metallurgical product properties have compelled the researchers to modify the conventional constant angle extrusion dies by employing streamlined die profiles. In the present research work, an optimum plane strain extrusion profile has been presented through implementation of upper bound analysis and Bezier curve in a simulated annealing (SA) algorithm to minimize the process force and its redundant work. The effect of material properties, friction conditions, reduction of area, and cross-sectional ratio on the optimum die profile is considered. The results of finite-element simulation proved that utilizing the optimum curved die instead of the constant angle die is superior regarding the decrease of the maximum required force, 10.5%, and the product inhomogeneity factor (IF), 50%. In addition, based on stress analysis of die/work piece interfaces, it is expected that the die life of optimal curved dies be longer than that of the optimum constant angle dies. Also, it has been demonstrated that the material work hardening characteristics does not have remarkable effect on the optimum curved die profile.