Wave propagation along a rectangular dielectric waveguide with slowly varying width has been studied using a transformed coordinate system and an effective cross-section approach. The associated differential equation has been solved using numerical analysis and Hill's analysis. The computed results have been verified using the cascaded transmission line matrix analysis of the structure in the original coordinate system. The agreement is found to be excellent. Many properties of the modulated periodic structure, for example, the propagation constant, the phase and the group velocities, the axial dependence of the Ell mode, and the space harmonic, have been studied. The results and the method will be useful in computer-aided design of dielectric waveguide phase shifters and filters. 0 1995 John Wiley & Sons, Inc.