During a manufacturing process, the shot peening technique can be used as the final surface treatment. The aim of this operation is to introduce surface compressive residual stresses in order to delay crack initiation and prevent its propagation. Although the numerical simulation method can predict the level of residual stresses in a peened part, the 3D modelling of the real process, in which many successive and shifted impacts take place, is very delicate to perform and costly in terms of computing time and resources. In the first part of this paper, a method which is applied in two steps is presented. The first step is based on the calculation of the averaged plastic strain tensor in a half-space by using a semi-analytical method. Secondly this plastic strain field is transferred to a finite element model in order to simulate the effects of the shot peening process in thin structures. The accuracy and advantages of the semi-analytical method are validated by a benchmark with several finite element codes. Experiments similar to the Almen test are performed on thin plates made of nickel base alloy. Numerical results in terms of distortions and residual stresses are compared with the experimental data. In the second part of the paper, some formulas based on digital plans of experiments are set up to obtain relevant information on the Process Affected Zone (PAZ) according to the impact parameters. For instance a relation between impact energy and indentation can be established to assess the surface roughness that is known to play a role on fatigue damage.