The problem of finding the response of a thick infinite plate to the application of body forces is considered. Transform techniques are employed to reduce the problem to that of an initial boundary value problem for a one-dimensional hyperbolic system. The latter is solved by the method of eigenfunction expansion. A representation of the displacement field is obtained which may be used to compute the transient response of the plate. As ab example we apply this method to obtain the plate response to the application of a point force. We discuss the computer implementation of this approach. Numerical simulations are presented for the case of an oblique force with a short burst time function.