In recent years, the study of acoustic scattering have provided a wide range of challenging problems for applied mathematicians, physicists and engineers. In this thesis, we consider two dimensional pentafurcated waveguides and parallel plate''s channel waveguide problems with different combinations of soft and hard boundary conditions by applying powerful eigenfunction matching or mode-matching technique. The reflected field amplitude behavior is depicted graphically for various dimensions for all these problems when the fundamental mode is assumed to propagate out of the mouth of the semi-infnite waveguide. Reflection and transmission by scattering and transfer matrices are also presented for parallel plate''s channel waveguides consist of single and double samples (scatters) by exploiting symmetry of the structures. We have shown how we can extend this work for multiple channel waveguide problems to reduce numerical and computational effort. This research work will be helpful for researchers to reduce unwanted noise effects in exhaust models, complicated devices and band stop filter analysis.