The spherical impact is a common phenomenon in mechanical engineering. The elasto-plastic impact is more complicate than the elastic impact. The elasto-plastic impact loads are investigated for the different contact stiffness and the different impact velocity by the nonlinear finite element method. The accuracy and reliability of the finite elements model are verified by comparing the numerical results of the elastic impact with the Hertz results. The elasto-plastic impact simulation shows that the impact loads have a negative exponential relation with the contact stiffness as well as a linear relation with the impact velocity. The contact time decrease with the increase of the contact stiffness and the impact velocity. The comparison between the influence of the contact stiffness and the impact velocity indicates that the impact velocity has a significant influence on the impact load and the contact stiffness has a big influence on the contact time.