Acoustic characteristics of silencer system are affected by various geometric parameters such as cross sectional geometry, size of chamber, and location of inlet-outlet port. It is impossible to obtain exact solutions of the equations of acoustic wave propagation except few simple cases. So, we resort to numerical techniques to analyze performance of acoustic system. In this work, finite element formulation has been obtained to predict transmission loss of an arbitrary 3-dimensional muffler in the presence of mean flow of low mach number. The effect of the degree of the ellipticity of expansion chambers on the transmission loss has been studied using the resulting finite element equation.