Reverberation from a rough elastic layered structure is formulated in terms of a self-consistent perturbation approach applied to the Green's function of a smooth elastic waveguide [W. A. Kuperman and Henrik Schmidt, J. Acoust. Soc. Am. 86 (1989)]. The acoustic field is decomposed into mean (specular) and scattered components, the generation of the latter causing the decay of the former. The scattered component is the reverberation in the waveguide, and computed examples are given. The mechanism for scattering from body waves into interface waves and vice versa is included in the formalism. Simulations of the scattered fields demonstrate this coupling between body and evanescent waves at rough interfaces separating elastic media. Reverberation can also be thought of as signal-generated noise and its structure is of interest when receiving signals in their reverberant background. Further simulations are presented highlighting this aspect of the problem.