A method for the derivation of the Green's function for a layered half-space loaded at its boundary is given in the contribution. We have limited ourselves to the forces with harmonic time dependence and to the out-of-plane stress case. We converted the leading differential equations into ordinary differential equations with the help of Fourier transformation and determined their solutions, which fulfill all boundary, continuity and radiation conditions. The solution thus obtained was then divided into a singular and a regular part. The inverse Fourier transformation, which completes the problem treated, is carried out for the singular part by transforming the integral path in such a way that we get a known integral representation of a Besse function, and for the regular part by numerical contour integration.