The aim of this work is to study the plastic instabilities occurring on the stamped sheets during deep drawing process. The analysis of the plastic deformation of the material showed that the deformation occurs in bi-axial extension at the bottom of the punch due to thinning of the sheet, in local necking together at the vertical wall level of the sheet and below the blank holder due to thickening of the sheet. As a first step, an experimental characterization of the material is undertaken, whose experimental tests made it possible to determine the fundamental characteristics of the material. In the second step, a study of the material behaviour during forming process by numerical simulation using Abaqus finite element code is proposed. The various simulations undertaken showed the variation of the two parameters; the blank holder force and the friction effect. The blank holder force and friction, applied respectively to the blank flange region and between the tool-blank surfaces, make it possible to optimize the deformation limits and to repel any instability which may appear on the material in deep drawing. The simulations carried out on Abaqus code allow to visualize the material behaviour during deformation, by locating the thinning and necking zones on the sheet and from there, in order to locate areas at risk of failure. An optimization of the process is proposed by varying the considered parameters in a validated numerical model. Satisfactory results have been obtained which clearly show the failure and the safe zones.