A fully framed system consisting of four beams and a rectangular plate has been investigated in terms of the energy transfer between the beams and the plate when a force is applied to one of the beams. This configuration, which is a mixture of stiff and flexible elements, is a particularly important example in the industrial area, as it is widely used. A modal model based on interface basis functions is used. A wave model, which is an approximate method, has also been developed in which the plate, acting as a wave impedance, is separately attached to each beam. Experimental studies have been carried out for validation. The investigation with respect to power flow and energy shows the validity of both models in the mid-frequency region. The results show that most energy is dissipated by the flexible plate. The physical phenomena and limitations of the wave method for this particular structural configuration are discussed. Even though it is an approximate method, the wave approach can describe the dynamic characteristics of the excited beam and the plate in terms of the ratios of power and energy of each component. The comparison of the two methods shows that the plate rather than the beams plays a crucial role in transferring the energy from the excited beam to the parallel opposite beam in the beam-framed structure when these two beams have identical properties, whereas the energy transfer is reduced when the beams have dissimilar properties.