The scattering and transmission of sound by an elastic spherical shell is considered when it is subject to an incoming monochromatic planar wave. It is aimed to cancel the sound scattering using combinations of multi-pole sources located at the centre of a shell filled with compressible fluid. Assuming linear acoustics and structural dynamics, exact solutions are derived for total elimination of the sound scattering for three cases: a free-space, near a hard ground or near a free-surface, where in the last two cases it is assumed that the incoming wave propagates normal to the interface to maximize sound reflection back unto the source of the incoming wave. An elastic spherical shell of 1 m radius embedded in water and filled with air or oil is analysed to show the dominance of low-mode numbers for frequencies of less than 10 kHz and thus demonstrate the ability of this approach to damp acoustic scattering by means of low-order multi-poles inside the shell. Contour and mode distribution plots are also given and analysed.