In this paper, the drawing process of the sheet metal through the wedge shaped die has been analyzed by upper bound method using stream function. First, a new deformation model has been introduced in which inlet and outlet shear boundaries are considered flexible. Then, the optimized geometry of the deformation zone has been determined through the effect of work hardening of the sheet material depending on the process conditions. According to the suggested stream function, velocity field, strain rates and power terms have been calculated. The analytical results have been compared with the results of the published analytical data and the finite element simulation results. Furthermore, the effect of work hardening exponent has been investigated on the deformation zone, drawing force and optimum die angle. It has been shown that by increasing the work hardening exponent, inlet and outlet shear boundaries of deformation zone are being inclined to the inlet zone of the die and the required drawing stress is decreased. In addition, by increasing the friction factor, inlet and outlet shear boundaries are being inclined to outlet zone of the die, and by increasing reduction in thickness, inlet and outlet shear boundaries of deformation zone are being inclined to the inlet zone of the die. It is shown that the analytical results have been improved up to ten percent in comparison to the published data.