Abstract: A semi-analytical approach is used to study the torsional vibration of a rigid circular foundation resting on poroelastic half-space subjected to obliquely incident SH waves. The Biot’s dynamic poroelastic theory is employed to characterize the saturated half-space. The governing equations for the saturated half-space and foundation are solved by using the Hankel transform. The total wave field in the saturated half-space is classified into free-field waves, rigid-body scattering waves and radiation scattering waves. According to the classification of the total wave field and the mixed boundary-value condition between the saturated half-space and foundation, the torsional vibration of the foundation is formulated into two sets of dual integral equations. Then, the integral equations are reduced to Fredholm integral equations of the second kind to solve. Considering the dynamic equilibrium equation of the foundation, the torsional vibration expression of the foundation is obtained. Numerical results are presented to demonstrate the effects of wave frequency, incident angle of the waves, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibration.