In order to obtain flawless pieces during the deep drawing process it is important to control the value of the blank holder force. An important value of the blank holder force limits the gliding of the steel sheet and develops its radial elongation. On the other hand, if it is not too big, the steel sheet can easily glide and the compressing stress which appears can cause the steel sheet's folding. The article presents the influence of the blank holder force on the variation of the cupped specimen's thickness in the case of cup drawing process. The results obtained through this simulation are compared to the experimental results. The simulation was performed by using the ABAQUS/Explicit v6.5 program.