The Boundary Element Method for Acoustics finds increasing applications in the automotive industry. The Boundary Element Method can solve two kinds of acoustical problems, including the passanger compartment noise, the induction noise, the exhaust muffler performance and the radiation noise of an engine or engine components. In this paper a resonator muffler element is discussed by using a Boundary Element Method code. This muffler element is a guide tube with holes passing through a cylindrical cavity. The impedance boundary condition on the hole surface is used so that the modeling of neck and cavity can be eliminated. Transmission Loss and distribution of acoustic patameters along the muffler element are estimated by BEM and compared with Plane Wave Solutions. The comparisons show good agreement.