Inhomogeneities in the earth’s crust and upper mantle have significant effects on surface wave characteristics such as phase and group velocities and amplitudes. In the last decade geophysical studies have shown that the earth’s crust is not only vertically but also laterally inhomogeneous. Many authors have already studied vertically inhomogeneous media by taking different variations. Some of the investigators have tried to discuss lateral inhomogeneity by taking vertical discontinuities in the earth. Alsop (1966) developed an approximate method for calculating reflection and transmission coefficients for Love waves incident on a vertical discontinuity. The concept of coupling coefficients between modes on either side of the boundary is introduced. Sinha (1964) discussed transmission of SH-waves in a homogeneous vertical layer sandwiched in a homogeneous medium. He obtained reflection and transmission coefficients for SH-waves incident normally in the planes of discontinuity. Singh (1974) studied Love wave dispersion in a transversely isotropic and latterally inhomogeneous crustal layer.