The solution is obtained for the transient response to a nontorsional surface load of an infinite. isotropic. elastic medium containing a cylindrical cavity with and without a thin elastic shell embedment using the Residual Variable Method. The main advantage of the present approach is that it eliminates the computational problems arising in the existing methods which are primarily based on the Fourier transformation technique. Numerical results for the displacements and stresses at different locations are presented for the case of a radial, Heaviside loading. (C) 1997 Elsevier Science Ltd.