A general analytical method, referred to as the Fourier spectral element method, is presented for the dynamic analysis of plate structures consisting of any number of arbitrarily oriented rectangular plates. The compatibility conditions between any two adjacent plates are generally described in terms of three-dimensional elastic couplers with both translational and rotational stiffnesses. More importantly, all plates involved can be arbitrarily restrained along any edges in contrast to the commonly imposed condition: each plate has to be simply supported along, at least, one pair of parallel edges. Thus, plate structures here are not limited to Levy-type plates as typically assumed in other techniques. The flexural and in-plane displacement fields on each plate are analytically expressed as accelerated Fourier series expansions and the expansion coefficients are considered as the generalized coordinates to be determined using the familiar Rayleigh–Ritz technique. The accuracy and reliability of the present method are validated by both finite element analysis (FEA) and experimental data for box structures under various boundary conditions.