A novel technique based on the Fourier transform is applied to analyze a ridge waveguide and rectangular coaxial line. On the basis of the image theorem the ridge waveguide and rectangular coaxial line are transformed into a guide with an infinite number of grooves. The dispersion relations for the ridge waveguide and rectangular coaxial line are obtained in rigorous, yet simple series forms. Numerical computations show that our series solutions converge fast and agree with others. ¿ 2001 American Geophysical Union