In this paper, we intend to propose a theoretical model which helps us precisely planning the servo press ram motion for a drawing process, and than the ductile fracture in drawing is supposed to be prevented effectively. The model is based on two important formability limits, including blanking reduction ratio and Cockroft's ductile fracture criterion. Experiments are performed for validation. We apply a servo press to perform the copper material drawing process with the ram motion according to the proposed model, and investigations of fracture initiation and drawability are discussed. The results show that we could draw the parts deeper without ductile fracture by adopting the proposed model. The model is contributive in improving drawing process, further it could be introduced into the control system of servo presses to facilitate ram motion planning.