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An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hubert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.