The merits and shortcomings are existed simultaneously in finite element method (FEM) and smoothed particle hydrodynamics (SPH) method, in which these methods are established based on Lagrange system. In order to makes use of high computational efficiency of FEM and advantages of SPH method, such as naturally simulation of large deformation of material, the coupling algorithm of FEM with SPH method is presented to calculate region of small deformation by FEM and simulate region of large deformation by SPH method. In this paper, the research and application of FEM, SPH and FEM-SPH coupling algorithm are reviewed. And the problems existing in these methods are also discussed. Finally, the computational accuracy and efficiency of FEM, SPH and FEM-SPH coupling algorithm are investigated by a numerical example, which is a reference for research fellows.