The main goal of this project is by using MPM which is in continuum formulation to reproduce the wear mechanism in larger scale simulation which is performed in atomistic scale by Professor Jean-François Molinari. Then, having experience and getting information about the Material Point Method (MPM) which is used for computational fluid dynamics and solid dynamics based on weak formulation which is also case for Finite Element Method (FEM). Short information about methods, mathematical aspects and algorithm are provided in this report. Then, comparison of MPM and FEM is included in terms of advantages and points for both methods. MATLAB is the tool for first and second examples. The code that developed by Tsinghua University is implemented for second and third examples. At the end, conclusion about the MPM is presented.