This article discusses the propagation of compressional waves in fluid‐saturated elastic porous media. Both harmonic and transient pulses are considered. In general, two modes of wave propagation exist. In the case of a transient pulse, these modes lead to a two‐wave structure. It is not possible to obtain closed‐form solutions for the general case of transient loading, but considerable insight may be obtained from certain limiting cases (e.g., no viscous coupling, large viscous coupling) for which analytical solutions are derived by means of Laplace transform techniques. Strong viscous coupling leads to the coalescence of the two wave fronts into a single front; in this case the material behaves like a single continuum with internal dissipation. Solutions for the general case are obtained both by numerical inversion of the Laplace transforms and by direct finite‐difference methods.