A mathematical model for the prediction of a safe zone for die cavity pressure and blank holding force/pressure, to avoid tensile and compressive instabilities in hydromechanical deep drawing is presented in this paper. Tensile instability is predicted using the load maximization principle whereas a solution for the stability equations provided the critical condition for compressive instability. Predictions of the present work are compared with results available in the literature and are in good agreement. A comprehensive parametric study is carried out to study the effect of process variables on the safe zone. © IMechE 2007.