We present a theoretical study of electromagnetic reflection and cavity modes of 1D-sub-wavelength rectangular metallic gratings exposed to TE-polarised light. Computations are made using the modal development proposed by Sheng et al .[Phys. Rev. B, 26 (1982), 2907--2916] and are a generalisation of those used by Barbara et al. [Eur. Phys. J. D, 23 (2003), 143--154]. In particular we study the influence of the choice of boundary conditions on the metallic surfaces on the mode coefficients.