The problem of wave propagation in a rod of viscoelastic material with step loading on the end is solved using realistic viscoelastic response characteristics covering approximately ten decades of logarithmic time. To overcome the inherent computational difficulties in the usual transform type of solution, an extension of the Schapery collocation inversion method to dynamic cases is proposed. The results indicate some material dispersion effects not evident in previous treatments using less adequate simple model representations. The present technique is also applicable to problems in two dimensions.