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In this paper, analytic formulations and their results are presented to extend the receptance method to a clamped–free cylindrical shell with a plate attached in the shell at an arbitrary axial position. Prior to the analysis of the combined system, the analysis of the free vibration for the shell without a plate was performed by the Rayleigh–Ritz method with a beam function. The integration of the beam functions was performed symbolically by Mathematica and was incorporated in a solution program that could be run in a personal computer. After getting the eigensolution of the simply supported circular plate, the frequency equation of the combined system was obtained by considering the continuity condition at the shell/plate joint. The numerical results were compared with the results from ANSYS, as well as a free vibration test, to validate the formulation. The comparison showed that the analytic results agreed with those from ANSYS and the test.