An efficient numerical approach, based on the boundary element method, for the analysis of electromagnetic field distributions in twodimensional tunnels with discontinuities such as L-bends, T-junctions, and cross-junctions is described. The side walls of the tunnels are assumed to be lossy dielectric and the surface impedance approximation is used to determine the boundary condition on the side walls. A computer program has been developed for tunnels excited by a line current or a TE dominant mode. A comparison of the numerical results with the experimental results using microwave simulation shows a good agreement except in the vicinity of the inner wall of the output tunnel perpendicular to the excited tunnel.