Abstract: The rocking vibration of a flexible circular plate with rigid core resting on saturated ground is studied.Based on the theory of elastic wave in saturated soil,the displacement solutions in Hankel transformed domain to the governing differential equations for saturated soil are obtained.With the assumption of adhesive contact between the plate and the ground surface,by keeping the rocking angle of the internal core constant and the flexible plate satisfying the equation of motion of a classic thin plate,dual integral equations which describe the mixed boundary-value problem for the plate are established.The equations are transformed to the second kind Fredholm integral equations.A numerical procedure is proposed to solve the equations.The dynamic impedance functions for rocking vibration are also derived.The effects of ground permeability,rigid core size and plate flexibility on the impedance functions are investigated and some meaningful conclusions are obtained.