The dynamic response of layered saturated soils to anarbitrary buried source is useful and important in seismology, seismicengineering, soil mechanics, geophysics, dynamic foundation theory and soon. Therefore, after Biot putting forward the general wave equations inisotropic saturated porous medium, there are a series of work on dynamicresponse in such medium by the FEM, BEM(in frequency space or Laplacespace), as well as analytical method(completed by Fourier expanding andHankel integral transformation). However, the most researches focus on theisotropic saturated porous medium less involving in anisotropic medium andexisting the limitations among the work mentioned above: the FEM relating toenormous amount of calculation as well as complex artificial boundary, theBEM involving in the completed dynamic singular close solution, which ishard to attain in layered saturated porous medium. Although the analyticalexpression in dynamic stiffness matrix containing $8(N+1)$ pendingcoefficients is given in Ref., it is an onerous work for computing$N$-layers saturated soils.The purpose of this article is to study the non-axisymmetical dynamicresponse of layered transversely isotropic saturated soils under anarbitrary buried source. In the first part, based on Biot's theoryfor fluid-saturated porous media, the 3-D wave equations in cylindricalcoordinate for transversely isotropic saturated poroelastic media aretransformed into the 1-order governing differential equations completed bythe Fourier expanding with respect to azimuth. Then, transfer matrixeswithin layered media are derived by introducing combined state vector andHankel integral transformation. The second part gives the analyticalexpression in dynamic response for multilayered such medium using transfermatrixes followed by boundary conditions and continuity conditions as wellas drainage conditions. In the third part, some numerical results arelisted. Time-domain results may obtain by Fourier synthesis over frequency.