Deep Drawing with rubber components of the conventional methods to remove the cost of manufacturing and is also an increase in LDR. The punch or matrix that is made of rubber.Deep drawing two sheet layers is one of the new methods to achieve desired properties in manufactured components. In this method two metal sheets together by glue connected to each other which together form the shape. Thinning control specially when the two materials or two different thickness is used, a single layer is different.In this paper the technique the initial gap used is between blankholder and fixed ring. In this study a square sample using die with rubber matrix with experimental and three-dimensional simulated, has been formed.In this paper, using the finite element method and model of hyper-elastic, three-dimensional simulations performed. Then, for verification,a die made with rubber components for cups square for both aluminum and sheets that by permutation method the practical experiments were perfromed and to compare the experimental and numerical results. Finally,with the help of response surface method collection simulations and practical experiments to evaluate parameters such as radius of punch, permutation the material type and the initial gap between the blank holder on the thinning, the force of punch and force blank holder performed.