The pressure in the scattered wave resulting from irradiation of an infinitely long, circularly cylindrical, thin isotropic viscoelastic shell by a plane monochromatic sound wave is calculated. The shell is assumed to be freely suspended in an ideal fluid and to enclose a second ideal fluid. The motion of the shell is described by means of Lagrange's equations, altered so as to account for viscoelasticity. The result for the scattered wave has the form of that for the elastic case except that an expression involving elastic constants is replaced by an impedance function involving viscoelastic parameters. Some properties of this impedance function are drawn from electrical circuit theory and used in discussing the usefulness of the viscoelastic parameters relative to modifying the scattered wave.