This paper studies torsional wave propagation in a poro-viscoelastic medium of finite thickness. The considered medium is clamped between an inhomogeneous poro-elastic medium of finite thickness and a poro-elastic half-space. Both finite layers are initially stressed and the half-space is self-weighted. Classical dynamical coupled theories have been used to explore the problem. Interior deformations are calculated analytically. A complex frequency equation has been obtained with the aid of suitable boundary conditions. The decomposition of the complex frequency equation into real and imaginary parts provides dispersion and damping equations. These frequency equations exhibited their reliance on the variation of attenuation coefficient, dissipation factor, inhomogeneity, initial stresses, Biot's gravity, porosity and thickness ratio parameters. The impacts of the aforesaid parameters have been extensively studied and demonstrated graphically. © 2020 Informa UK Limited, trading as Taylor & Francis Group.