The radar cross section (RCS) of a circular waveguide terminated by a perfect electric conductor is calculated by the geometrical theory of diffraction (GTD) for the rim diffraction and by a physical optics approximation for the interior irradiation. The interior irradiation is generally more than 10 dB higher than the rim diffraction for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a/\lambda \geq 1</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</tex> is the waveguide radius, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> is the free-space wavelength). At low frequencies ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a/\lambda \sim 1</tex> ), the interior irradiation can be significantly reduced over a broad range of incident angle if the interior waveguide wall is coated with a thin layer (1 percent of the radius) of lossy magnetic material. Our theoretical prediction is confirmed by measurements. At higher frequencies ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a/\lambda \sim 3</tex> ), a thin layer of coating is effective for the case of near axial incidence, provided that a good transition of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TE_{11}</tex> mode near the waveguide opening to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HE_{11}</tex> mode inside the waveguide is made. A thicker layer of coating is required for the RCS reduction over wider incident angle.