Electromagnetic wave scattering from a dielectric‐coated sinusoidal diffraction grating is considered. The incident field is assumed to be TE (P) polarized. The analysis technique is based on the extended boundary condition method. Numerical tests show that both energy conservation and reciprocity principles are obeyed. Mode coupling efficiencies as a function of angle of incidence are presented for dielectric coated gratings consisting of: (i) a perfect conductor, (ii) silver, and (iii) aluminum. These three cases exhibit anomalous behavior at a predicted angle of incidence.