A wave approach is used in the Statistical Energy Analysis (SEA) of a system comprising two, edge-coupled, simply supported, rectangular plates. The response of the system is described in terms of ''wave components'', each associated with a unique trace wavenumber along the coupling. An ensemble of plate systems is defined, and analytical expressions are found for the ensemble average input and coupling powers which result from ''rain-on-the-roof'' excitation of one of the plates. Two parameters which quantify the strength of coupling between plates are found, and four distinct regimes of wave component energy flow and storage are observed, involving weak and various forms of strong coupling. For the system considered, the plates may be wholly weakly coupled (all wave components are weakly coupled), or the response may involve some mixture of weakly and strongly coupled components. In the case of the latter, the response is normally dominated by the strongly coupled components. The coupling is found to be strong in most systems of practical interest. The traditional SEA hypothesis of proportionality between the coupling power and the difference in subsystem mean modal energies is found to hold for the ensemble average response, for all coupling strengths, but not generally for the responses of individual ensemble member systems. A coupling loss factor is found, defined in terms of the ensemble averaged response. The traditional estimate of coupling loss factor, found by a wave approach in which semi-infinite subsystems and diffuse fields are assumed, is seen generally to be an over-estimate of the true value for the present system, except when the coupling is weak. It is also found that modal overlap, which has been proposed as an indicator of coupling strength and of the accuracy of the traditional coupling loss factor estimate, is inappropriate in this role for the rectangular plate systems considered.