When a Rayleigh wave becomes “supersonic” for a given geometry of propagation, a thin solid layer coated on the surface of the medium can bring about the transformation of this wave into a leaky wave. In such a case in the sagittal plane there emerges a narrow interval of angles of incidence within which the phase of the reflection coefficient suffers abrupt changes, and the reflection is accompanied by excitation of surface vibrations with amplitudes greatly exceeding the amplitude of the incident wave. The effect is due to the resonance excitation of the leaky wave. The critical angle of incidence and the width of the resonance interval are determined by the real and imaginary parts of the leaky wave speed. Approximate expressions for the leaky wave speed and for the coefficients of plane wave conversion are derived and analyzed without any assumptions about the crystallographic symmetry of both the substrate and the layer.