A coaxial line flush mounted on an infinite perfectly conducting ground plane and covered by a dielectric hemisphere is investigated. Green's functions for the region above the ground plane are derived with separated homogeneous and particular solution parts so as to be compatible with numerical analysis techniques. A magnetic field integral equation is obtained in terms of the unknown annular aperture tangential electric field and is solved by the method of moments. A comparison between the present case and that of a flush-mounted coaxial line with an infinite homogeneous region above the ground plane is presented in terms of the tangential aperture electric field, the coaxial line apparent input impedance and the far radiated field.