The propagator matrix method is used to solve the problem of the static deformation of a transversely isotropic and layered elastic half-space under the action of general surface loads. The solution is obtained in two systems of vector functions for different cases of characteristic root determined by the elastic constants of the media. It is shown that this general solution contains, as its special cases, the solutions obtained by previous researchers, such as the solution for isotropic and layered media, and the solutions for the problems of axially symmetric and two-dimensional deformation of transversely isotropic and layered media. Numerical examples are given to verify the present formulation. It is noted that by using the propagator matrix method in two systems of vector functions, the present analysis method is efficient, convenient and easy to apply in practice.