Summary: The aim of this study is to simulate the dynamic vertical response of an unsprung mass, i.e. wheel, traversing a beam, i.e. bridge or rail. This is achieved by using the authors’ modal or finite element method to model the dynamic interaction that exists between the unsprung mass and the beam. In this paper, the authors compare the final form of the modal method with the final form of the finite element method, and they clearly demonstrate that if the mode shapes of the modal method are replaced by the finite element weighting and shape functions, the finite element method is derived, apart from the stiffness matrix. The results for the moving load compare very well with J. E. Akin and M. Mofid’s solution [Numerical solution for response of beams with moving mass. J. Struct. Eng. 115, No. 1, 120–131 (1989)]; however, the results for the moving mass are very different. Other authors who are getting agreement with Akin and Mofid’s (loc. cit.) moving mass are ignoring the issue of convective acceleration.