In this project thesis, initial blank shape optimization of a twin elliptical cup to reduce earring phenomenon in anisotropic sheet deep drawing process was studied .The purpose of this study is optimization of initial blank for reduction of the ears height value. The optimization process carried out using finite element method approach, which is coupled with Taguchi design of experiments and reduced basis technique methods. The deep drawing process was simulated in FEM software ABAQUS 6.12. The results of optimization show earring height and, in addition, a number of design variables and time of process can be reduced by using this methods. After optimization process with the proposed method, the maximum reduction of the earring height would be from 21.08 mm to 0.07 mm and also it could be reduced to 0 in some of the directions. The proposed optimization design in this article allows the designers to select the practical basis shapes. This leads to obtain better results at the end of the optimization process, to reduce design variables, and also to prevent repeating the optimization steps for indirect shapes.