The study of periodic media is mainly focused on one-dimensional periodic structures (periodic along one direction), to determine the dispersion curves or for the calculation of the response to an external excitation. Effective methods such as the Wave Finite Element (WFE) have been obtained for such computations. Two-dimensional periodic media are more complex to analyse but dispersion curves can be obtained rather easily. Obtaining their response to an excitation is much more difficult and the results mainly concern infinite media while for finite media, few results are available. In this communication, the response of finite two-dimensional periodic structures to an excitation is studied by limiting oneself to structures described by a scalar variable (acoustic, thermal, membrane behaviour) and having symmetries. Using the WFE for a rectangular substructure and imposing the wavenumber in one direction, we can calculate the wavenumbers and mode shapes associated with propagation in the perpendicular direction. By building solutions with null forces on parallel boundaries, we can decouple the waves in the two directions parallel to the sides of the rectangle and solve each case by a FFT. Summing the contributions of all these waves gives the global solution with a low computing time even for a large number of substructures. Examples are given for the case of a two-dimensional membrane.