To investigate the high-frequency vibration and acoustic radiation of fluid-loaded structures, the model problem of a simply-supported plate excited by a random pressure field is considered. The analysis is standard and yields a set of modal equations coupled by acoustic interaction terms. These terms not only complicate the equations, but also appear in a form that is difficult to evaluate numerically at high frequencies and mode numbers. The latter problem is resolved by deriving asymptotic expressions for the acoustic coefficients, and computational solution of the full, coupled modal equations then becomes feasible. By comparing the results with the `diagonal approximation' (the solution when coupling is ignored), an improved characterization of the physical nature of the acoustic coupling is obtained, and new conditions for its neglect are specified. The conditions are not stringent, implying that the diagonal approximation will often be valid, and raising the possibility of applying statistical energy analysis (SEA) to significantly fluid-loaded structures. Modified SEA results are derived, and found to compare well with the modal solutions.