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A procedure for computing characteristic modes for the problem of electromagnetic coupling to arbitrary shape conducting objects behind arbitrary shape apertures in a conducting body is developed starting from the operator formulation of the currents. The mode currents are obtained from the admittance and impedance operators. This formulation is general and characterized by its simplicity and efficiency. This method is applied to a finite thin wire backed by a rectangular aperture in a conducting plane in an unbounded medium. The integral equations in terms of the magnetic and electric current distributions are derived for the magnetic and electric fields. The moment method is used to obtain matrix equations approximating the integral equations. The expansion functions are chosen to satisfy the continuity equations and to vanish at the wire endpoints. Finally, modal solutions are computed to illustrate the convergence of the solution as the number of modes increases.