We use an approximate method to study the reflection and transmission of obliquely incident Rayleigh waves on a vertical boundary between two welded quarter-spaces. For two media with a phase velocity ratio of 1.16 our calculation shows that the transmitted energy follows a reciprocity relation and decreases from near 100 per cent at normal incidence to 50 per cent at about 40°. The reflected energy is less than 1 per cent for angles of reflection less than 40°. When the Rayleigh wave impinges upon the less rigid medium, the reflected energy decreases as the angle of incidence increases; whereas for incidence at the more rigid medium, the reflected energy decreases at first, and then it increases as the angle of incidence increases. Since boundary conditions on the free surface are not taken into account by our method, diffraction effects are ignored. The effect of neglecting the free surface requirement is difficult to quantify, but we believe that it is small since the calcualted and experimental results agree well at normal incidence.