This paper deals mainly with the dynamic response of a rigid disc bonded to the surface of a layered poroelastic half-space. The disc is subjected to time-harmonic torsional moment loadings. The half space under consideration consists of a number of layers with different thickness and material properties. Hankel transform techniques and transferring matrix method are used to solve the governing equations. The continuity of the displacement and stress fields between different layers enabled derivation of closed-form solutions in the transform domain. On the assumption that the contact between the disc and the half space is perfectly bonded, this dynamic mixed boundary-value problem can be reduced to dual integral equations, which are further reduced to Fredholm integral equations of the second kind and solved by numerical procedures. Selected numerical results for the dynamic impedance and displacement amplitude of the disc resting on different saturated models are presented to show the influence of the material and geometrical properties of both the saturated soil-foundation system and the nature of the load acting on it. The conclusions obtained can serve as guidelines for practical engineering.