Laser shock peening attracts increasing attention as one of techniques to improve fatigue life of materials and structures. The application of this technique generally induces a compressive residual stress field, modifies the geometrical shape and alters the material hardening. Nanosecond laser peening, which uses nanosecond laser pulse is necessary to be carried out in immersed water for the confinement of the plasma. On the other hand, femtosecond laser peening, which uses femtosecond laser pulse, can be carried out in the air because of its high laser intensity. However, both techniques proceed under a very high strain rate, making difficult to completely understand the whole peening process, therefore the best conditions for laser peening and the mechanism of creation of residual stress field have not been clarified well yet. In this study, finite element analyses are carried out to examine the residual stress field, displacement and distribution of equivalent plastic strain in order to examine the effect of laser peening on the material properties. Each technique was simulated by means of a single laser shot irradiating to the center of the specimen surface. We discuss the numerical results of the residual stress, displacement and equivalent plastic strain fields.