The Problem of mechanical vibration is investigated for an automotive exhaust system. The vibrational reduction effect is systematically evaluated according to the attachment of the exhaust system. Moreover, the optimal attachment position of bellows is determined from the viewpoint of vibration isolation. The structure is analysed by the finite element technique where the geometry, the mass, the stiffness and the damping properties of the exhaust pipe are modeled. The validity of the developed model is verified by comparing with the experimental results. An optimization is carried out by the quadratic approximation algorithm. The reaction transferred to an automobile body by the hanger is considered ad the objective function. It is shown that the exhaust system which has the bellows at the optimal position is more effective for the vibrational characteristics than the others. It is also proved that this analytical method is quite useful in the design stage of the exhaust system.