The light diffraction on dielectric grating placed on metallic substrate by the method of coupled waves (CWM) taking into account the 53 diffraction orders is analysed. The modified stable S-algorithm is used for diffraction analysis. At certain parameters of grating the resonance of coupled waves (CWR), which consists in sharp increase of electromagnetic field into grating, appears. This increase of electromagnetic field results in full absorption of wave energy in metallic substrate. The behaviour of CWR depends on modulation value of permittivity of grating material. The approximate grating parameters at the condition of appearance of waveguide effect corresponding to CWR are found. These parameters are improved for achievement of full absorption by the picking-up method. The grating parameters on platinum, potassium, gold, silver for wavelengths of 0.85 μm and 1.5 μm at condition, that reflection coefficient less that 0.0001, by CWM are found. For Pt and K the dependencies of reflection coefficient on the grating thickness for TE and TM polarisation are obtained. For all metals dependencies of reflectance on wavelength, which it is possible rather precisely to describe by analytical equations with a Laurence's function, are calculated. Especially, analytical dependence precisely coincides with a curve, which by CWM for grating with small permittivity modulation of grating material is obtained. For potassium and silver the dependence of reflectance on light incidence on grating is obtained. The analysis of resonance absorption effect for TE and TM polarisation is conducted.