In this paper, basing on Hu haichang’s theory and using Fourier transformation, the problem is changed into solving fourth-order and second-order linear ordinary differential equations. The eigenvalue method is used for solving these equations, and then both displacement and stress with undetermined coefficients can be received. Considering the boundary conditions, the exact displacement and stress of the transversely isotropic foundation can also be gotten. Especially on the transversely isotropic elastic half space, with the aid of computer software, a more simple vertical displacement is presented. When the foundation is degenerated into isotropic elastic half space, the displacement is also degenerated into elastic half space displacement in a rectangular coordinate system which is given in the reference. And this exactly proves the result which is received from this paper is right. On this basis, we can analyze a settlement of transversely isotropic foundation and the static characteristics of rectangular plate on the transversely isotropic foundation.