In this paper, a hybrid Mode/Fourier-transform approach is described for estimating the vibration response of a structure such as a beam-stiffened plate with excitation applied to the beam. The beam is defined deterministically in terms of its modes, whereas the plate is treated approximately by assuming it extends to infinity. Equilibrium and continuity conditions are approximated along the interface between the beam and the plate in the wavenumber domain by a Fourier transform method. Consequently, both the dynamic response of the beam and the power transmitted to the plate can be simply estimated. Meanwhile, the dynamic interactions of the coupled system can be determined. These depend on the correlations between the modal properties of the beam and the wave motions of the plate. Expressions are given for the effective mass (density) and effective loss factor the plate applies to each mode of the beam. When a locally reacting plate approximation is incorporated into the Mode/Fourier-transform procedure, a simpler ‘locally reacting impedance method’ can be developed. The results are discussed and compared to those of fuzzy structure theory. Numerical examples are presented.