A theoretical study is made on the scattering of a Rayleigh wave which is incident on a rough semi-circular surface. Partition of energy fluxes of the waves scattered by the semi-circular rough surface is obtained. It is then revealed that the resonances of P and S waves occurring in the semi-circular body considerably suppress the transmission of the incident Rayleigh wave through the semi-circular rough surface, while the Rayleigh wave resonance appearing along the curved free surface of the semi-circular body strengthens the transmission of the incident Rayleigh wave. Directivity of the energy flux of the waves scattered into the semi-infinite elastic body is also discussed; partition of the energy fluxes of the waves scattered into two quarter spaces which are on the incoming and leaving sides of the incident wave greatly depends on two factors, the relative size of the semi-circular body to the wavelength of the incident Rayleigh wave and the appearance of the resonance of the Rayleigh wave in the semicircular body. In the semi-infinite elastic body, the zone of high energy density of the scattered S waves runs at an angle of 45° to the plane free surface; this zone is named breathing zone, since the zone is produced as the results of the interchange of energy between the generated Rayleigh waves and the scattered S waves. As for the phase lag of the transmitted Rayleigh wave, it is retarded in the range of kb_??_1, 0 (k: wave number of the incident wave, b: radius of the semi-circular rough surface) owing to the generation of retarded waves in the semi-circular body, while it is advanced in the range of kb_??_1.0 due to the appearance of the P and S waves which are transmitted through the medium below the semi-circular body directly from its front root to the rear root.