The cross-section method is an analytical tool used in the design of components required for low-loss, highly efficient transmission of electromagnetic waves in nonuniform waveguides. When the waveguide dimensions are large compared with the wavelength, a fully three-dimensional analysis employing modern numerical methods based on finite element, finite difference, finite integration or transmission line matrix formalisms is practically impossible and the cross-section method is the only feasible analysis technique. The method is not limited to oversized tubular metallic waveguides, but is employed intensively in areas such as fibre optic communications, antenna synthesis, natural waveguides (submarine, tropospheric and seismic), microwave radio links (Earth or space) and the design of absorbing surfaces and it may also be applied to many acoustic problems. The application of the method in special cases such as cut-off and resonant frequencies is covered, as well as the design of oversized waveguide components such as tapers, bends, polarisers and mode converters. Many useful formulas are given for the practical layout of such transmission line components. The use of computers in the application of the method and problems related to numerical analysis are also covered.