A numerical scheme effective in dealing with a class of two-dimensional open waveguide problems is summarized in this paper. It involves initially a decomposition of a given problem into several elementary waveguide discontinuity problems so that characterization of each individual one is known analytically in the spectral domain independent of its excitation. Governing equations for spectral components in the coupling regions connecting adjacent waveguide discontinuities are then derived and solved numerically. The asymptotic behavior of unknown spectral components usually can be derived from related edge conditions and used effectively to improve the convergence of the solution.