The moment method is used to solve the electric-, magnetic- and combined-field integral equation, to determine the current distribution on a semi-infinite, open-ended, circular waveguide. A standard triangle-function expansion is used to represent the exterior waveguide wall currents. The approximate nature of this current distribution is shown to lead to difficulties with the uniqueness of both the solutions associated with the electric- and magnetic-field integral equations. By examining the degree to which the boundary conditions are satisfied, the combined-field integral equation is shown to yield superior results.