The application of the angular spectrum of plane waves, previously shown by Robinson, and Hamid for the problem of mode propagation in a rectangular waveguide loaded with a single E plane dielectric slab, is extended to an arbitrary number of slabs. The technique employs ray optics and residue calculus and is developed to the point where considerable theoretical advantages are evident when dealing with the more general case of a waveguide loaded with an arbitrary number of lossy or lossless dielectric slabs and excitation by a discrete set of propagating modes or inhomogeneous line sources. To illustrate the procedure for the case of three slabs, the dispersion equation for the modes in one slab is derived and the computed eigenvalues are verified by comparison with the recent results of Gardiol, based on a matrix boundary-value solution, and Kashyap and Hamid, based on a perturbation analysis. The transverse electric-field distribution is extended to the other slabs so that the boundary conditions at the interface of two planar dielectric slabs are satisfied. Plots of the transverse electric field due to propagating modes for a particular case are also presented and shown to converge when only the first few modes are considered. It is found that the frequency bandwidth, defined as the separation between the cutoff frequencies of the dominant and next highest-order mode, may be increased or decreased over the unloaded waveguide depending on the physical dimensions and relative permittivity of the slabs.