Deep drawing process to produce square cup is very complex process due to a lot of process parameters which control on this process, therefore associated with it many of defects such as earing, wrinkling and fracture. Study of the effect of some process parameters to determine the values of these parameters which give the best result, the distributions for the thickness and depths of the cup were used to estimate the effect of the parameters on the cup numerically, in addition to experimental verification just to the conditions which give the best numerical predictions in order to reduce the time, efforts and costs for producing square cup with less defects experimentally is the aim of this study. The numerical analysis is used to study the effect of some parameters such as die profile radius, radial clearance between die and punch, blank diameter on the length and thickness  distributions on the cup, dynamic-explicit (ANSYS11) code based on finite element method is utilized to simulate the square deep drawing operation. Experiments were done for comparison and verification the numerical predictions. effective square cup with less defects and acceptable thickness distributions were produced in this study. It is concluded  the most thinning appear in the corner cup due to excessive stretching occur in this region and also it is found the cup thickness and height prediction by numerical analysis and in general in harmony with experimental analysis.