DescriptionThis thesis provides an extensive review of acoustic wave theory in one, two (polar), and three (spherical) dimensions concluding with a study of passive, non-directional cloaking. The optical theorem is derived by use of energy conservation, yielding the cross sectional scattering in two and three dimensions. A new method, the Matricant Propagator, is developed for solving the scattered pressure field in wave-object interactions. Solutions found from the Matricant Propagator method are compared with known solutions using the Global Matrix method. A review of acoustic cloaking literature is given, including numerical comparison with previously proposed cloaking models. Lastly an acoustic cloak of the inertial type, made from compressible, inviscid fluids, is proposed by layering concentric shells of only three distinct fluids. The effectiveness of the device depends upon the relative densities and compressibilities of the three fluids. Optimal results are obtained if one fluid has density equal to the background fluid, while the other two densities are much greater and much less than the background. Numerical examples display a significant reduction in scattering and were compared using multiple solution methods. It is found that use of only two unique fluids is too restrictive for cloaking, however, interesting characteristics are found where energy may be diverted such that a reduction in backscatter occurs.