Fatigue failure occurs in components subjected to cyclic loading in various applications. To reduce the fatigue failure of components compressive residual stresses in the material plays an important role. There are mechanical surface treatment processes to induce compressive residual stress in the materials up to certain depth by which fatigue life of the component can be increased. Among that, Laser shock processing (LSP) is one of the surface treatment processes that improve fatigue life of the component. In LSP, a target component coated with a sacrificial layer is subjected to high power laser short duration pulse. This causes shock waves which induce compressive residual stresses in the component. For optimising the LSP process parameters simulation is widely used with complex physics model of the process and predict its outcome. This paper discusses the various input parameters required for LSP simulation and the commonly used mesh representations and material models. It also reviews the different simulation procedures used to simulate single as well as multiple laser impacts. © 2016 Elsevier Ltd. All rights reserved.