Flanged parallel-plate radiation of a TM-wave into a dielectric slab is investigated. The Fourier transform is used to represent the radiation field in the spectral domain and the boundary conditions are enforced to obtain the reflection coefficient in rapidly converging series form, Numerical computations are performed to illustrate the radiation behaviour in terms of aperture size, frequency, and slab geometry, It is found that a single-mode approximate solution predicts well the radiation behaviour when a flanged rectangular waveguide is excited in the TE(10) mode.