Peening is a major principle of improving the characteristics of critically loaded components of the systems. By this process we introduce into the material compressive residual stress, which has a positive influence on the life of parts. In the literature, it can be found that peened austenitic steel can transform some of its crystal lattice in into the martensitic. There is a big difference between the two procedures, conventional shot peening, for which the literature describes a substantial amount of martensite formed, and the laser shock peening in which it is rarely possible to observe martensite. With the help of a constitutive model that describes the behavior of austenitic stainless steel AISI 304 on a macroscopic level we ran an dynamic analysis of these two types of peening in Abaqus software environment. From observed stress field, the residual stresses, plastic deformation and the resulting amount of martensite can be concluded that the main reason for such a significant difference is in the duration of the load and in the stress deviator. We also compared the values for certain material points from the analysis to analiticly calculated functions for a given stress state, which showed satisfactory accuracy of the simulation.