In shallow water or fluid half-space, the acoustic scattering from a target is significantly different from that of an unbounded medium, due to the multiple reflections occurring between the target and the boundaries. The purpose of this thesis is to investigate the influence of the boundaries on the acoustic scattering of a rigid sphere by means of a superposition method. A minimum number of point sources necessary to accurately model the scattered field is determined in the case of a free medium, a fluid half-space and a waveguide. The free field symmetry vanishes due to the presence of boundaries and, at particular frequencies or scatterer depths, a significant change in the magnitude and spatial distribution of the scattered field occur. In an unbounded medium or fluid half space, the superposition method is shown to give similar results to analytical formulations found in the literature, provided enough point sources are used.