This paper is concerned with the computational procedure of displacements and stresses of an elastic multi-layered half-space due to harmonic loads acting in the interior of the half-space. In calculating the fundamental solutions of displacements and stresses, the authors propose a transfer matrix method taking advantage of a vectormatrix form which expresses the general solutions of displacements and stresses being used in the derivation of dispersion function of an elastic multi-layered half-space. The results shown in this paper can be used as the fundamental solutions in the Boundary Element Method. As numerical examples, the stresses of an elastic half-space due to vertical and horizontal concentrated loads are calculated for the various non-dimensional frequency ωH₁/V_s1.