A result is proved that the singular pointsηE and ηH of the boundary integral equations of the outer scattering fields E

z

￣（s）and H

z

￣（s） of a cylindrical conducting surface are equal. Then a method for solving the cutoff wave numbers of waveguide is suggested

in which the same one program may be used commonly for E mode and H mode. The only change needed is the adjustment of the sign of the main diagonal elements. The cutoff wave numbers of E mode are also the singular points for the outer scattering problem.