The aim of this investigation is to compare the classical St. Venant’s solution of the axial impact on flexible rods with the numerical result from a finite element computational procedure involving component mode synthesis. A new technique developed to simulate impacts is used to this end. The impacts treated are those mainly governed by the propagation of elastic waves along the complete flexible body. Local effects at the vicinity of the contact surfaces are neglected. The phenomenon of succession of impacts is analytically proved, a second period of contact is found in a particular case. A numerical method is developed to solve the collision based on the theoretical solution. This technique is able to identify the elastic waves which travel along the rod and a force balance is continuously made to yield the contact stress and the velocity of the surfaces in contact. Numerical solution shows an excellent agreement between the numerically obtained displacements histories with the theoretical results. The capability of the eigenvectors to describe the wave propagation is analysed as well as the effect of the elements boundaries.