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We propose a new hybrid MoM formulation for the analysis of scattering from dielectrically-covered finite arrays of cylindrical cavities in an infinite ground plane, illuminated by a plane-wave source. The new formulation focuses on the use of techniques that maximize both the accuracy and efficiency of the numerical computations. As a result, the algorithm is quite useful for analyzing rather large yet finite structures without resorting to approximate methods. The hybrid approach is both more accurate and efficient than purely numerical solution techniques. Hence, the method has the additional capacity to serve as a useful benchmarking application for other less accurate numerical algorithms.