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One of the main problems in the design of exhaust silencers is the attenuation of low frequency noise. At these frequencies is where the influence of the engine has more importance; moreover, low frequency noise has the possibility of interaction with the mechanical resonances of the exhaust line, producing additional noise and vibration highly disturbing. A suitable solution to this problem is the use of the interferencial behaviour between two acoustic parallel paths, which produces high attenuation at a given frequency associated with the difference between the acoustic lengths of both paths. In the present paper, a general expression for the 4-pole transfer matrix of an interferencial system with two arbitrary branches is presented, which is applied to a simple but realistic exhaust silencer. Results are compared with the transmission loss measured with a modified impulse method, with good agreement between the model and the measurements.