Bu using the perturbation method, the sound wave propagation equation in the medium with a linear temperature gradient is simplified into Helmholtz equation, which can be computed numerically with the boundary element method. The four-pole parameters of muffler can be obtained using BEM, therefore the acoustic characteristics such as transmission loss can be predicted. The four-pole parameters of a straight duct and transmission loss of an expansion chamber have been calculated and compared with the results obtained by means of one-dimensional theory.