This paper is concerned with investigating the difference in response between a three-ply elastic plate of infinite lateral extent and a similar plate in which the core elastic layer is replaced by a layer of viscoelastic damping material. The transient response of the plate to an impulsive loading is governed by the dispersion equations for infinite trains of harmonic waves propagating under traction free conditions on the plate surfaces (see e.g. Achenbach [1]). These dispersion equations express the wavelength and the damping factor as functions of the frequency and they possess an infinite set of roots, corresponding to different modes of wave motion. In addition to their relevance to the impulsive loading problem, the dispersion curves of the various modes, have a significance for the experimental determination of the properties of laminates by ultrasonic techniques (see e.g. Mal and Bar Cohen [2]).