In this article, the propagation of torsional surface wave in an anisotropic poroelastic layer of finite thickness sandwiched between two heterogeneous dry sandy media is investigated. The first uppermost dry sandy medium is considered as a layer of finite thickness and the second one is considered as a lower half-space. The heterogeneities in both dry sandy media are assumed to arise due to quadratic variations in elastic moduli and mass densities. Whittaker’s functions and variable separable techniques have been taken into the application to calculate the interior deformations inside the assumed model; consequently, we obtain a closed form dispersion relation for the torsional wave using effective boundary conditions. Moreover, casewise dispersion equations for some particular aspects of the problem have been studied, which serve as the focal theme of the study. Some significant observations have been made by detailed numerical calculations and graphical visuals related to the effects of tensile and compressive initial stresses, sandy parameters, heterogeneity parameters, porosity parameter, and thickness ratio parameter on the phase velocity of the torsional wave. © 2017 Informa UK Limited, trading as Taylor & Francis Group.