Abstract: A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetical harmonic source.However,the assumption may not always by valid.The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetical harmonic force.The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established.By the techuique of Fourier expansion and Hankel transform,the governing different equation for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained.Then,under the contact conditions,the problem leads to a pair of dual integral equations which describes the mixed boundary-value problem.Furthermore,the dual integral equations can be reduced to the Fredholm integral equations of the second kind and solved by numerical procedure.At the end,a numerical result is presented which indicates that on a certain frequency range,the displacement amplitude of the surface of the foundation is increased with the increase of the frequency of the exciting force,and decreased in vibration form with the increase of the distance.