Abstract: By introduction of transmitting matrices’technique for layered structure,mixed equations with stresses and displacements are derived from the basic equations of transversely isotropic elasticity.Then,using Fourier transformation and the general solutions in Zhou et al.[7],the point force solution for transversely isotropic elastic layer is obtained and it can be degenerated to the corresponding solution of isotropic medium. In this paper,all equations are derived by the use of computer algebra software.