A theoretical treatment of sound transmission through the walls of non-circular muffler shell is done for plane mode transmission within the muffler shell. Non-circular muffler shells include distorted circular (due to the welding seam), elliptical (oval) and flat-oval shells. An analytical formulation has been developed in this thesis in order to predict the breakout noise with the acoustical and structural wave coupling phenomena. First, progressive wave model is chosen. Then, the Transverse Transmission Loss (TTL) is predicted at different frequencies of interest. This formulation is extended to the standing wave model by which results for anechoic, rigid end and open end boundary conditions are obtained. Transverse transmission loss (TTL) predicted, based on the analytical model, is compared and validated with computational results using a commercial 3-D numerical simulation (vibro-acoustic) software package like SYSNOISE. Same model is used for non-circular shell with flat-oval configuration. And also breakout noise obtained from different configurations like circular, elliptical, flat-oval, rectangular and square, all having the same equivalent radius, are compared. Finally, by incorporating effects of finite length of the muffler and end plates, analytical model has been developed for a circular shell. Parametric studies have been done wherever required to evolve the design guidelines which will be helpful for designers.