The boundary-value problem of scattering from an annular slot on a radial waveguide is solved. The scattered fields are expanded in terms of eigenfunctions based on the Fourier series and Hankel tran, form. Boundary conditions are enforced to constitute a set of simultaneous equations. A fast convergent series solution is obtained using residue calculus. Computations are performed to investigate radiation and coupling by an annular slot on a radial waveguide. Favorable agreement is observed between our theory and other existing results. (C) 2005 Wiley Periodicals, Inc.