An analysis is made of the distribution of intensity of the evanescent waves in a semi‐infinite elastic medium when a plane acoustic wave in a contiguous fluid medium is incident upon it. It is found that the maximum intensity and total energy in the evanescent wave occurs at the angle of incidence corresponding to the Rayleigh angle [θR = sin−1(C 0/CR), whereCRis the Rayleigh wave speed andC0is the sound speed in the fluid medium]. This result gives insight both mathematically and physically as to what should be expected for surfaces with curvature as well as for plates.