The propagation of a cylindrical wave in an infinite viscoelastic (standard linear) solid is studied by means of the Laplace transformation. Numerical results are obtained over a time interval encompassing the most significant characteristics of wave propagation, namely, attenuation of the initial peak, formation of the delayed peak, and asymptotic decline to the steady state. It is found that no marked change in the wave shape occurs until the distance from the axis exceeds a certain characteristic length (which is infinite in a perfectly elastic solid) and that the change becomes more marked at greater distances.