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A mathematical model has been developed for the investigation of mechanical vibrations of an exhaust system under road load excitation. For practical reasons, the vehicle body and the exhaust system has been considered as masses connected by springs and dampers. Non-linear damping characteristics of the vehicle tires and the exhaust isolators have been included in the model. Equations of motion have been solved in the MatLab environment, and transfer functions of the system and response to input signals representing the power spectrum density (PSD) of the road profile have been obtained for each mass in the system. The model developed has been verified through comparisons to the acceleration time history recordings on a proving ground and has been used for the parametric studies. The paper describes a comparison of model results with experimental observations, and predictions of parametric studies.