A simple and efficient numerical solution method is presented for the problem of a flanged parallel-plate waveguide whose aperture is loaded from the exterior by a dielectric semicylinder of arbitrary cross-section. The exterior half-space of the waveguide also contains a nearby conducting cylinder, which is disjoint from the dielectric load. According to the equivalence principle one shorts the guide aperture and places equivalent magnetic currents on opposite sides of the slot. By using image theory and the surface equivalence principle, which employ only equivalent electric currents at the material interface, one obtains a set of coupled integral equations in terms of the aperture electric field and equivalent currents on the cylinders. Data are presented to show the effect of conductor and dielectric loading on the aperture electric field, the current on the conductor, the reflection coefficient and the radiation pattern for TEM-wave excitation from within the waveguide.