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Above the cut-off frequency of the first acoustic cross mode, the modeling method considering only the plane-wave propagation completely fails to carry out an accurate prediction of the actual silencing ability even for the acoustically long chambers. In this paper, the mathematical expressions of transfer matrices, or so-called four-pole parameters, for several reactive silencer elements are shown as the results of the three-dimensional acoustic analysis of the cavity in circular-cylindrical chambers. The theoretical results are compared with the measured transmission losses and they are in good agreement. Some idealizations involved in deriving the formula are discussed and the applicability of the results is briefly commented.