This paper reports on the use of mathematical modelling by the GPB method of pressure wave propagation through finite systems, for the design of prototype exhaust systems and silencers for a Harley-Davidson motorcycle. The motorcycle engine is the classic 1340 cm3 45° V-twin power unit. The design objectives were to gain mid-range power and torque without loss of performance at either end of the speed range and to design silencers which would enhance the performance and the noise image of the machine.The Queen's University of Belfast (QUB) (3)* employed their unsteady gas flow modelling techniques to the design of the system and its silencers to complement a new camshaft design from Crane Cams. The results of the use of these computer based design techniques are reported as performance characteristics of power and torque for the new design by comparison with the stock system. The comparisons reported are both computed performance characteristics and for those measured experimentally on a chassis dynamometer.Also shown are the computer predictions for the pressure diagrams at the exhaust valve for the stock and the QUB systems, which pressures heavily influence the ensuing airflow through the engine and the torque which is subsequently attained.The design of the silencers enhances the behaviour of wave action within the exhaust system, so that the engine produces more power and less noise with silencers fitted to the QUB system by comparison with open straight pipes. Measurements are provided to illustrate this point.