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Background: Today, the most common method for kidney stone therapy is extracorporeal shock wave lithotripsy. Current research is a numerical simulation of kidney stone fragmentation via ultrasonic shock waves. Most numerical studies in lithotripsy have been carried out using the elasticity or energy method and neglected the dissipation phenomenon. In the current study, it is solved by not only the linear acoustics equation, but also the Westervelt acoustics equation which nonlinearity and dissipation are involved.Objective: This study is to compare two methods for simulation of shock wave lithotripsy, clarifying the effect of shock wave profiles and stones' material, and investigating side effects on surrounding tissues.Material and Methods: Computational study is done using COMSOL Multiphysics, commercial software based on the finite element method. Nonlinear governing equations of acoustics, elasticity and bioheat-transfer are coupled and solved.Results: A decrease in the rise time of shock wave leads to increase the produced acoustic pressure and enlarge focus region. The shock wave damages kidney tissues in both linear and nonlinear simulation but the damage due to high temperature is very negligible compared to the High Intensity Focused Ultrasound (HIFU). Conclusion:Disaffiliation of wave nonlinearity causes a high incompatibility with reality. Stone's material is an important factor, affecting the fragmentation.