A current-expansion technique is proposed to analyze the waveguide discontinuities of irregular shape. Roof-top and rectangular-pipe sub-domain functions are used in an electric-field integral-equation formulation to adequately expand the three-dimensional current densities of an irregularly-shaped conductor. It is therefore applicable to quite general discontinuity configurations. Numerical results for a variety of waveguide discontinuities including open-ends, bends, and T junctions have been demonstrated and verified by the available published data.