On account of some complexities such as fluid-structure interaction and extra-large deformation problems, complete simulation of abrasive water jet cutting process is very hard. The main goal of this paper is to overcome these difficulties through comprehensive simulation in LS-DYNA commercial software. For this purpose the Smoothed Particle Hydrodynamics (SPH) and Arbitrary Lagrangian Eulerian (ALE) methods are employed. Utilizing these methods, the depth of water jet penetration and mechanism of erosion are simulated for a certain test case. In addition, the effect of water pressure and traverse speed on depth of penetration are examined. Comparison between the obtained results using both methods showed that the numerical results are in good agreement with available experimental data.