The present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). Both the half-spaces are assumed to be under compressive initial stress. The study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. The dispersion relation of torsional surface wave has been obtained in the presence of heterogeneity, initial stress and anisotropic, and it is observed that the inhomogeneity factor due to quadratic and hyperbolic variations in rigidity, density and initial stress of the medium decreases the phase velocity as it increases. The result also shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. In the absence of anisotropy, Initial stress, inhomogeneity and rigidity of the upper half-space, then the dispersion relation coincide with the classical dispersion relation of Love wave. پرونده مقاله