Abstract: Based on the theory of elastic wave in saturated soils established by the first author of this paper,the vertical vibration of a rigid circular footing resting on saturated soils is studied.At first the governing differential equations for saturated soils are solved by Hankel transform.Then,considering the boundary condition,the dual integral equations of vertical vibration of a rigid circular footing resting on saturated soils are established which are reduced to Fredholm integral equation of the second kind.The dynamic compliance coefficients for the saturated soils and the amplitude of the vibration of the footing versus the dimensionless frequency a 0 are presented at the end of the paper.