In this paper we have discussed the propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half space with initial stress. The method of separation of variables is applied to find the dispersion equation. Numerical results analyzing the dispersion equation are discussed and presented by means of graphs. The effect of reinforcement, inhomogeneity parameter and the initial stress on the propagation of torsional surface wave is the main objective in our study. It has been observed that the directional rigidities of the half space have a favoring effect on the phase velocity, whereas the density and initial stress parameter in the half-space have the adverse effect on the velocity of torsional surface wave. It is remarkable to quote that reinforcement prevails in the medium, the phase velocity increases significantly.
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