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The electromagnetic field coupling through small apertures illuminated by an arbitrary incident plane wave is discussed for general aperture shapes. A set of new integral equations in a form highly amenable to numerical solution techniques is derived. Based on the application of the Rayleigh series method, an analytical solution is obtained for the first few terms of the expansion of the aperture - field of a circular aperture. Numerical results are also constructed for the aperture field and the diffracted field of small rectangular apertures and compared with those of the circular apertures.