With considering the vertical heterogeneity of soil layers and the feature of torsional vibration, the dynamic motion equations of a generalized Gibson saturated soil are developed. Then the proposed equations are solved by using the integral transformation. Given the stress-free boundary condition at the top surface of the saturated half-space, the mixed boundary condition in the plane where the rigid circular plate is laid, and the wave radiation condition at the infinite depth, the dual integral equations are developed to depict the torsional vibration of a rigid circular plate embedded in a generalized Gibson saturated soil. By appropriate transformation, a Fredholm integral equation of the second kind is obtained; and the dynamic response of the soil is determined. The dynamic compliance coefficient and the torsional angular amplitude is formulated by comparing the relation between a static torque and angular displacement. The problem can be degenerated into a simple case, which is consistent with previous research results. Numerical studies indicate that there exists a boundary-layer phenomenon in the torsional vibration of a rigid circular plate in a generalized Gibson soil when the embedment depth is five-times smaller than the radius of the circular plate; in addition, the smaller embedment depth, the more pronounced the boundary-layer phenomenon is.