Experimental analysis can be very costly and time consuming when searching for the optimal process parameters of a new shot-peening configuration (new material, new geometry of the part...). The prediction of compressive residual stresses in shot-peened parts has been an active field of research for the past fifteen years and several finite elements models have been proposed. These models, although they give interesting qualitative results, over-estimate, most of the time, the level of the maximal compressive stresses. A better comprehension of the phenomena and of the influence of the parameters used in the model can only carry a notable improvement to the prediction of the stresses. The fact that the loading path is cyclic and is not radial led us to think that a model including kinematic hardening would be better adapted for the modelling of shot peening. In this article we present the results of a simulation of a double impact for several constitutive laws. We study the effect of the chosen constitutive law on the level of residual stresses and, in particular, we show that kinematic hardening, even identified on the same tensile curve than isotropic hardening, leads to lower stress levels as compared with isotropic hardening, Furthermore, the overall shape of the stress distribution within the depth is significantly different for the two types of hardening behaviour. Further, in order to check the modelisations, local measurements were carried on with X-ray diffraction on a large size impact and correlated with the topography of the impact.