The scattering of a plane wave by a thin spherical shell surrounding a solid sphere is determined. The results are given for shells of uniform thickness and axially symmetric cases for shells of nonuniform thickness. For a shell of uniform thickness the method of separation of variables can be applied, but for shells of nonuniform thickness the more general method described must be used. Numerical results are given for the scattering coefficients, target strength and farfield pressure distribution. It is shown that replacing a solid sphere by a thin spherical shell of the same diameter which surrounds a smaller internal solid sphere can lead to variations in the target strength of the order of ±10 dB. The results depend on the interaction between waves reflected from the inner body and the shell. Thus, important parameters are the spacing between body and shell and the wavelength. As body spacing and frequency are increased, the effect is to increase the average target strength.