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An arbitrary shaped cross-sectional discontinuity in rectangular waveguides is investigated using FEM-BIM with triangular prism elements, which is more effective than normal FEM. The volume of the discontinuity is subdivided into a relatively small number of triangular prism elements and FEM is used to formulate the field distribution. On the other hand, the fields in the waveguide region are represented by BIM derived from the waveguide Green's function and boundary conditions. The proposed method is verified through experiment for the circular iris in a WR-90 waveguide.