Abstract: MPM(Material Point Method)is a new meshless method.Evolving from the Particle-in-Cell method.It takes advantage of both Eulerian and Lagrangian methods,and its background mesh is simply divided.All variables of material points are mapped on to background mesh by shape functions.Strain and stress values of material points under impact load are calculated by governing equations and constitutive relation.The deformation and fracture of continuum are expressed by the material points coordinate,and background mesh is fixed in whole calculation process.The basic theory of MPM is introduced in this paper.Two numerical examples,stress wave propagation in long bar and the damage of concrete wall under impact load,are studied using the method.