This paper derives the guided‐mode extracted boundary integral equation (GMEIE) for the basic theory of computer‐aided design of complex electron waveguide circuits. The derived integral equation is amenable to direct numerical analysis by the method of moments (boundary element method) without using the modal expansion. If the electron energy is larger than the external potential of the waveguide so that the electrons are radiated outside the waveguide, the problem can still be coded by using an algorithm almost identical to the one for the case where electrons are trapped inside the waveguide. The characteristics of the two‐port electron waveguide circuit with a finite external potential of the waveguide are analyzed and the mathematical validity of the integral equation as well as the effectiveness of the method are studied. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(6): 43–51, 2000