Source problems in homogeneous and inhomogeneous isotropic media have been discussed by many investigators since the classical paper by Lamb (1904). The displacements have been studied by considering different types of fixed or moving sources. A brief account of these investigations has been given by Ewing, Jardetzky and Press (1957). Miira (1958), De (1969), Vlaar (1966, a, b) and others have studied the displacements of SH-waves in heterogeneous isotropic media. Mitra (1958) has found normal medes and surface displacements for SH-waves from a prescribed surface traction in a half-space. The variations of rigidity and density in the half-space are assumed to very as exp (az) and exp (Bz) respectively, z being the depth coordinate. De has considered the medium in which the density and rigidity both vary as exp (2 z). Vlaar (1966) has discussed the displacements due to SH-waves from the point source in a (i) layer and (ii) half-space in which rigidity and density are assumed to be piece-wise continuous functionsof depth. He has studied the normal modes as functions of the source depth and frequency by using Strum Liouville’s Theory of eigenfunction expansion. Sidhu (1971) and Bhattacharya (1973) have discussed SH-waves from torsional sources in a semi-infinite elastic medium. Bhattacharya (1973) has obtained displacements in a homogeneous isotropic half-space due to torsional disturbance produced by an expanding source. He has derived the solutions for two different cases where (i) the velocity of the expansion of the source is less than that of shear-waves in the medium (ii) the velocity of expansion of the source is greater than that of the shear-waves in the medium. He has used integral transform technique and the modified Cagniard method. Sidhu (1971) obtained the formal solution ofthe displacements field due to SH-waves from burried, time harmonic, torsionel sources in a half-space in which a and p vary continuously with depth. He has applied this formal solution to study the SH-waves from a torsional source in a half-space in which u and p vary exponentially with depth.