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A method is proposed for predicting the radiation pattern of rectangular apertures on a finite rectangular ground plane. This method includes an accurate description of single, double and vertex diffraction mechanisms. The first step of the analysis is the full-wave estimation of the aperture field. To this end, the external and the internal regions are separated by replacing each aperture with a metallic plug with equivalent magnetic currents on its external and internal sides; these currents are of equal amplitude and of opposite sign to ensure the continuity of the electric tangential field through the aperture. Then, an integral equation is formulated, that represents the continuity of the tangential H-field through the apertures. To solve the internal-external coupling, the external flange is initially treated as an infinite ground plane. After the determination of the magnetic currents, these currents are considered as radiating on the finite ground plane. For the sake of simplicity, but without loss of generality, a single horn is considered. The internal region of the corrugated horn is analyzed by using a generalized admittance matrix method.