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The principal aims of this paper are twofold: 1) to solve the problem of the scattering of a thin, perfectly conducting aonular strip suspended in a multimodal circular waveguide in which any number of TE0n modes can propagate, and with the aid of this result, 2) to give the susceptance of the thin annular strip in monomodal circular guide with an incident TE01 mode. These are treated with a variational approach. Applying the appropriate Green's functions to the continuity equations for the transverse electric field yields a variational expansion for the scattering matrix elements. This is treated with a Rayleigh-Ritz procedure and matrix methods. Curves of normalized susceptance as a function of the free-space wavelength and the size of the annular metallic strip are shown. These results are in good agreement with experimental data. Tables of the scattering coefficients for a typical wavelength versus strip size are also included.