The detailed theoretical analysis of the resonance phenomena caused by excitation of the surface Josephson plasma waves (SJPW) in layered superconductors is made. It is shown that the surface waves at the boundary between the vacuum and layered superconductor can be excited by attenuated total reflection (ATR). The dispersion relation for the SJPW and the intensity of the reflected wave are investigated. The parameters of the problem (optimal thickness of vacuum layer, optimal wavelength) corresponding to the total suppression of specular reflection (TSSR) are found