The aim of this study was to apply an approximate Galerkin finite-element method to solve the initial boundary-value problem of a viscously damped axially moving pre-tensioned beam including arbitrary support excitations. In order to validate the Galerkin finite-element method the results were compared with exact solutions when available and with solutions obtained using the finite-difference and Galerkin methods. The energy dissipation of the system was considered in the form of an equivalent viscous-damping model. It was also shown that for certain values of the parameters, especially at high velocities, the Galerkin method using stationary string eigenfunctions can give a poor prediction of the dynamic response.