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Cavity-backed microstrip patch antennas are often used in aircraft applications because of their ability to conform to the vehicle surface. For arrays of patches, it is important to be able to predict the dependence on surface curvature of the coupling between patches. The mutual impedance between two rectangular patch antennas recessed in an elliptic cylinder is computed using a finite element-boundary integral method. Results show that the coupling between the antennas is dependent on the curvature of the cylinder surface. For H-plane coupling, the coupling decreases as the radius of curvature increases. For E-plane coupling, the strongest coupling occurs for a specific curvature.