The farfield acoustic radiation efficiency and power of a flexible rectangular plate coupled to a relatively stiffer beam are investigated. A numerical model based on a modal method that consists of a plate with sliding edges surrounded by four stiff beams is studied. Assuming that each beam is a heavy mass, a plate with clamped edges is realised, and this model is verified. This model is then extended to a beam-stiffened plate. If the bending stiffness of the excited beam is large, the radiation efficiency increases in the corner- and edge-mode frequency regions and is higher than that of the clamped plate in terms of the averaged response for randomly selected excitations. The reason for this effect is that the corner and edge areas that radiate sound are broader because the behaviour of the plate is governed by the motion of the stiff beam. This is explained in terms of the wavenumber and the wavelength of a stiff beam and a flexible plate. It is shown that this is true only when the excitation is applied to the beam, and the radiation efficiency is similar if the plate is excited. In addition, it was found that the radiation power decreases with increasing beam stiffness because the vibration of the plate actually decreases. In addition, it was shown that the variation in the radiation efficiency of the beam-stiffened plate is smaller when the beam is excited than when the plate is excited.