The acoustic power radiated by a rectangular plate bounded by a uniform mean flow is investigated. Asymptotic expressions for the modal radiation efficiency of a simply supported plate are derived, and confirmed by comparison with numerical results. The asymptotic expressions show that the frequency at which a mode becomes an efficient radiator is reduced in the presence of mean flow, and hence that the critical frequency for a vibrating elastic plate is similarly lowered. The effects of these changes on the radiation damping of an aircraft panel in cruise, and on its radiation efficiency on landing, are investigated. The asymptotic results are then extended to more general plate edge conditions via analysis of appropriate infinite and semi–infinite problems. Hence the ‘3 dB rule’, that a plate with clamped edges, vibrating well below the critical frequency, radiates twice the power of a plate with simple supports, is shown to apply also in the presence of mean flow.