We are interested in the problem of a buried antenna, where an antenna A is located in a volume D dug in the ground. The ground is assumed to fill the half space zlt;0 in three dimensional coordinate space (z, y, z), and to be homogeneous with a dielectric constant /spl epsiv//sub 1/. The volume D is filled with a homogeneous medium /spl epsiv//sub 2/. To simplify the calculations, we choose a cylindrical symmetric configuration with and cylindrical hole of radius d and depth H and an axial vertical dipole antenna of length L. Our solution strategy is based on decomposing the problem into simpler subproblems. This method has been used in corresponding two dimensional problems such as apertures in infinite conducting surfaces. The solution progresses along three steps as described. (1) First we construct an exact spectral integral solution for the dyadic Green's functions in the unperturbed air-ground configuration. (2) Next we find the dyadic Green's functions for the composite configuration. (3) Finally we solve the antenna problem (i.e. the current distribution and the input impedance) by solving an integral equation on the antenna surface, using the Green's function. This Green's function is also used to calculate the field radiated by the current distribution on the antenna.