Laser shock peening (LSP) is a mechanical surface treatment that induces plastic deformation and compressive residual stress in the material similar to shot peening. Pressure generated by the pulsed laser is far above the yield stress of the material and pulse duration is on the order of nanosecond. Finite element analysis is applied to simulate LSP and predict plastic deformation and residual stress through different constitutive models. The development of analytical model including model details, loading time history and constitutive model equations and parameters is discussed. Finally, results are presented for different constitutive models and experiment results are discussed.