The objective of this investigation is to develop a finite element computational procedure for the analysis of impact-induced transverse waves in articulated mechanical and structural systems. This procedure is based on the generalized impulse momentum equations that involve the restitution condition. The accuracy of the finite element solution is established using a simple linear model which has a closed form solution. The use of the procedure developed in this investigation is demonstrated using a rotating beam subjected to transverse impacts. The dispersive nature of the transverse waves in rotating beams is examined, and it is shown that the phase velocities of the waves have different frequencies which depend non-linearly on the wavenumber as well as the angular velocity of the beam. Furthermore, as the angular velocity increases, the phase velocities of the transverse waves decrease and, in general, the finite rotation has more significant effect on the phase velocity of low frequency transverse waves as compared to the high frequency waves. The equations of motion that include the effect of the centrifugal forces resulting from the finite rotation of the elastic beam are developed using the principle of virtual work in dynamics. In order to establish the accuracy of the numerical procedure developed in this investigation, the solution obtained using the finite element method is compared with the solution obtained using the eigenfunction expansion. Numerical results show that there is a good agreement between the finite element and the eigenfunction solutions. However, these results indicate that for the same number of modes, the finite element solution propagates faster than the eigenfunction solution.