A hybrid technique which utilises the finite element method (FEM) and an expansion of the field in terms of the Floquet modes is presented for the analysis of the scattering from and through periodic structures, having arbitrary geometry, material properties and periodicity with respect to the wavelength. This formulation can play an important role in validating approximate methods and in the analysis of the interaction of an electromagnetic wave with complex periodic structures. The periodic boundary conditions which are imposed for applying the FEM procedure are discussed in detail. Numerical results for bothTEZandTMZscattering are presented.