Shot peening is a mechanical surface treatment widely used in industry to improve the fatigue life of metal components. During the process, hard shots hit the surface of the treated mechanical part at high velocity, locally introducing a residual stress field due to plastification effects. To optimize the process, several analytical and numerical models have been proposed. Existing simulations show their efficiency to better understand the mechanism of residual stress introduction and better evaluate the influence of the shot peening parameters on the residual stress profile. Because the shots used in shot peening are always harder than the treated material itself, a classical approach consists in using a rigid sphere model in the computation; it is indeed usually necessary to introduce simplifying hypotheses due to the relative complexity of the process. During the industrial process, the shots may, in fact, be elastically and plastically deformed. Then, the impact will print a weaker dent in the material and the residual stress profile will be affected accordingly. Thus, it seems interesting to quantify these effects and we propose a finite element model for shot peening where the influence of the parameters associated to the shots, that is to say the velocity, radius and yield stress, are carefully analyzed. To better understand the process, we propose to compare the results of finite element models in which several sets of material parameters have been considered for the shots and the treated part. Several values of the shots' velocity and radius, chosen among the values commonly used in industry are considered. The resulting residual stress profiles are presented. It appears that the residual stress profiles in the solid are indeed sensitive to the shots' yield stress; this effect can be significant.