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A simple numerical solution is given for the problem of a parallel-plate waveguide with a slot covered by a dielectric semi-cylinder of arbitrary cross-section. The exterior half-space of the waveguide contains also a perfectly electrically conducting (PEC) cylinder, which is disjoint from the dielectric cover. The excitation is an incident TEM wave from within the waveguide. The surface equivalence principle is used to obtain a set of coupled integral equations in terms of the aperture electric field, and the equivalent electric currents on the PEC and the dielectric cylinder. The integral equations are solved numerically by the method of moments. For several practical cases, the effects of conductor and dielectric loading on the reflection coefficient and radiation pattern data are presented along with the aperture electric field and cylinder currents.