Far-field backscattering from a perfectly conducting cylinder with a surrounding shell has been investigated. The spacing of the shell from the cylinder and thickness of the shell are arbitrary. The material in the shell is also arbitrary and is characterized by the propagation constant h. The incident plane wave is at right angles to the cylinder, and is either horizontally or perpendicularly polarized. When the shell is thin in units of wavelength a much simpler expression for the backscattered field coefficient is obtained. It was possible to express this coefficient in a form which resembles the coefficient from the conducting cylinder alone plus a perturbation term due to the shell. Another simplification resulted when the propagation constant h of the shell is much larger than the free-space propagation constant k.It was desirable to see what scattering properties a cylinder with a surrounding shell exhibits. The cylinder was chosen to be large with respect to wavelength and the shell spaced a resonant distance from the cylinder. The scattering cross section, for this particular combination of parameters was then given by a slowly converging series which proved too lengthy for hand-computation, and was then programmed for and computed by the IBM 704. The scattering cross section versus shell spacing is shown in graphical form.