In order to solve the problem of collision in engineering field, the dynamic equation of collision system was established based on FEM(finite element method) and contact element model. The present method can account for the influence of the nonlinear contact stiffness as well as the energy loss during collision process. Collision had been simulated using FEM and MSM(mode superposition method) separately with various contact stiffness, sphere masses and impact velocities. The results indicate that FEM can be used to solve the problem of collision. The two groups of time history curves of contact load have almost the same shape. Compared with the results by MSM, collision durations are relatively decreased by about 7%, and difference of peak value is no more than 4%. The method can be used for collision between two complex structures with nonlinear reaction. So, it has a wider application to simulation of collision damage in engineering field.