A mathematically simple procedure was developed that secures a great increase in the range of wedge angles for which numerical computation of the reflection and transmission coefficients of Rayleigh waves in a wedge-shaped medium can be performed. Whereas in previous research the range of angles in such a medium for which computation was possible was treated as necessarily lying between 72° and 108°, the present procedure extends that range to between 36° and 180°. Furthermore, by completely separating the poles located on the original integral path, it becomes possible to perform numerical calculations on the original path itself. The numerical results thus obtained were found to coincide almost perfectly with experimental ones. It is pointed out that in cases of wedge angles exceeding 180°, the present procedure allows a greater extension of the computable range than was previously possible. Moreover, the features of scattered body waves inside wedges are discussed over the wide range of wedge angles.