This thesis endeavors towards developing various concepts employed in analysis and design of acoustic filters for varied applications ranging from combination mufflers for automobiles to complex networks of gas carrying ducts to multiply connected complex automotive silencing devices to the noise control coatings for underwater applications. A two-dimensional wave modeling approach has been proposed to evaluate sound attenuation characteristics of dissipative mufflers of finite length with/without extended inlet and outlet tubes including very large mufflers. The correctness of the method has been validated through comparison with experimental results from literature. Two other frequently used approximate schemes have been discussed briefly with reference to the available literature. These three approaches have then been weighed against each other to show the effectiveness and limitations of each one. A thorough comparison study has been performed to investigate each one’s extent of applicability. A parametric study with different parameters suggests some useful design guidelines that can be put to use while designing such mufflers. Benefits and drawbacks of reactive and dissipative mufflers have been discussed with an intention of striking a compromise between them to achieve a better transmission quality over a broad frequency range. This has been accomplished by combining these two types of mufflers/filters explicitly. These combination mufflers are analyzed using a transfer matrix based approach by extending the aforesaid concept of two-dimensional wave modeling for finite dissipative ducts. The present approach has been used to analyze axi-symmetric circular lined plenum chambers also. The effectiveness of the bulk reaction assumption to model absorptive lining is illustrated. A parametric study has been carried out to investigate the effects of different thicknesses and placements of the absorptive lining. The contributions of reflective and absorptive portion of the combination mufflerto overall attenuation performance have been investigated from the designer’s point of view A generalized algorithm has been developed for studying the plane sound wave propa- gation in a system of interconnected rigid-walled acoustic filter elements. Interconnection between various elements is represented by a connectivity matrix. Equations of volume velocity continuity and pressure equilibrium at the interconnections are generated using this connectivity matrix and are solved using the Gauss-Jordan elimination scheme to get the overall transfer matrix of the system. The algorithm used for generalized labeling of the network and computation of Transmission Loss has also been discussed. The algorithm has been applied to investigate a multiply connected automobile mufflers as a network of acoustic elements which guides the way to a specialized application discussed next. Results for some configurations have been compared with those from the FEM analysis and experiments. A parametric study with respect to some geometric variables is carried out. The acoustical similarity between apparently different networks is discussed. The approach is flexible to incorporate any other acoustic elements, provided the acoustic variables at the junctions of the element can be related by a transfer matrix a priori. Commercial automotive mufflers are often too complex to be broken into a cascade of one dimensional elements with predetermined transfer matrices. The one dimensional (1-D) scheme presented here is based on an algorithm that uses user friendly visual volume elements to generate the system equations which are then solved using a Gauss-Jordan elimination scheme to derive the overall transfer matrix of the muffler. This work attempts and succeeds to a great extent in exploiting the speed of the one dimensional analysis with the flexibility, generality and user friendliness of three dimensional analysis using geometric modeling. A code based on the developed algorithm has been employed to demonstrate the generality of the proposed method in analyzing commercial muffers by considering three very diverse classes of mufflers with different kinds of combinations of reactive, perforated and absorptive elements. Though the examples presented in the thesis are not very complex for they are meant to be just representative cases of certain classes of mufflers, yet the algorithm can handle a large domain of commercial mufflers of high degree of complexity. Results from the present algorithm have been validated through comparisons with both the analytical and the more general, three-dimensional FEM based results. The forte of the proposed method is its power to construct the system matrix consistent with the boundary conditions from the geometrical model to evaluate the four pole parameters of the entire muffer and thence its transmission loss,etc. Thus, the algorithm can be used in conjunction with the transfer matrix based muffler programs to analyze the entire exhaust system of an automobile. A different kind of acoustic filter than the above mentioned cases is then taken up for investigation. These refer to the specialized underwater acoustic filters laid as linings on submerged bodies. These kind of underwater noise control linings have three different types of objectives, namely, Echo Reduction, Transmission Reduction (TL maximization) and a combination thereof. These coatings have been shown to be behaving very differently with different shape, size and number of air channels present in the layer. In this regard, a finite element model based methodology has been followed. An hybrid type finite element based on the Pian and Tong formulation has been modified and used so as to make the computational efforts less demanding as compared to the original one. The developed finite element has been shown to be immune to the difficulties that arise due to the near incompressible characteristics of the viscoelastic materials used and the high distortion of the elements of the FE mesh. The adequacy of this formulation has been shown by comparing its results with the analytical, FE based, and experimental results. Then, this methodology has been used to analyze and generate design curves to control various geometrical parameters for proper designing of these linings. Different unit cell representations for different types of distributions of air cavities on the linings have been discussed. Four different types of layers have been introduced and analyzed to address different objectives mentioned above. They have been termed as the Anechoic layer, Insulation layer and Combination Layer of coupled and decoupled type in this thesis. The first two layers have been designed to achieve very dissimilar characteristics and the next two layers have been designed to balance their disparities. A thorough parametric study has been carried out on the geometrical parameters of all the layers to come up with the design guidelines. For anechoic and the insulation layers, different distributions have been analyzed with different unit cell geometries and their usability in specific situations has been outlined. Effect of static pressure has also been studied by using an approximate finite element method. This method can be used to simulate deep-sea testing environment.