Abstract: The two rods in colliding are treated to be an integrated rod system of vibration, so this nonlinear elastic impact problem is dealt with as a problem of conventional dynamic response analysis of the system under the initial condition that the impacting rod is subjected to a given velocity distribution. The basic equation, the boudary conditions and the initial conditions of the problem are given, the analytical solution without contact deformation and with linear contact deformation are derived, and the new linearization method and the practical procedure of the linearization method with nonlinear contact deformation of the problem are presented.Finally, numerical results show that the above methods and the approaching procedures are feasible and correct.