The theory of transmission of a plane dilatational wave through an infinite plane layer is considered where the three media involved are assumed to be linearly viscoelastic, their properties being specified by four elastic constants. Relations for the complex transmission and reflection factors are obtained as well as for the intensity relations and specific acoustic impedance in the incident medium. The equations of state for a viscoelastic fluid and viscoelastic solid are used to relate the basic elastic constants to the basic propagation constants for the media. The transmission relations are then given in terms of these propagation constants. Computed transmission characteristics for water through steel into air and for water through rubber into air are presented and the dependence of these characteristics on the dissipative properties of the media are shown. These numerical examples illustrate the transition of transmission properties in going from low‐frequency, thin plate conditions to high frequency, thick plate conditions. Special relations for these limiting conditions are also given.