AbstractA method for rigorous analysis of transmission in and radiation from a uniformly bent finite‐length section of a slab wave length is proposed. The eigenmodes with continuous eigenvalues, which are similar to the radiation modes of the straight waveguide, are defined first for expressing fields in circular bends of slab waveguides, and a kind of orthogonality relation for these eigenmodes is derived. The spectral integral of these eigenmodes can give a rigorous expression of fields in circularly bent sections, which is proved by using the radiation condition and the Fourier transformation technique. The theory is applied to the analysis of transient phenomena of fields in the uniformly bent section connected to the straight section. Numerical examples of transition of field distributions and radiation patterns are presented and the results are discussed in detail.