Abstract: The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground is studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soil were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth,and the state equation was established by Hankel integral transform method,furthermore the transfer matrixes within layered media were derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions,drainage conditions on the surface of ground as well as the contact conditions.Thirdly,the problem was led to a pair of dual integral equations describing the mixed boundary-value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end,a numerical result concerning vertical and radical displacements of both the surface of saturated ground and plate was evaluated.