This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous isotropic porous material having a rigid frame. The coefficients of the propagation equation are constant and depend only on the acoustical parameters of the porous material. The propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method. An experimental application to porous plastic foams is given to validate the solution of the propagation equation. (C) 2003 Elsevier Science B.V. All rights reserved.