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Using a finite element approach, a technique for optimization of an exhaust system design was developed. This technique involved the creation of the parameterized model, implementation of the loading and finally the optimization of the model. In the creation of the finite element model, pipe elements were used. Parameters were assigned to the structure using coordinate relations between nodes, instead of the positions of the nodes in coordinate space. The model was then verified using modal analysis. A random vibration analysis was used as a loading criterion for the model, as well as static gravitational loading. The optimization of the design focused primarily on the shape characteristics of the structure and secondarily on each component thickness. Using only thickness parameters, a 15% reduction of the weight of the system was achieved, with an additional 2-3% decrease in weight possible through shape optimization.