Under the excitation of an engine, an exhaust system vibrates, and the vibrational energy is transmitted to the vehicle body through the exhaust mounts. The transmitted energy makes contribution to the vibration of the body, which in turn increases the overall vehicle noise level. Noise contributed by the exhaust can be eliminated up to a certain level by reducing the force transmitted through the exhaust mounts. In this study, an objective function, which represents the force transmitted through the exhaust mounts, is defined. The aim is to minimise the transmitted force to achieve better vibration isolation. First, structural dynamic analysis of the vehicle exhaust system is evaluated using computational and experimental procedures. The finite element model of the exhaust system is complemented and validated by following an experimental modal analysis procedure. In the correlation procedure, it is observed that boundary conditions of the exhaust system have significant effects on the results. Hence, the definitions and the assumptions of boundary conditions are studied in detail to achieve a better correlation between the computational and the experimental models. Then, the validated computational model is used for optimisation studies. Moreover, a mass is attached to the exhaust system to reduce the forces transmitted to the vehicle body. For the optimisation problem, the stiffness and the location of exhaust mounts and the weight and the location of hanging mass are defined as design variables. Significant improvements are achieved compared to the initial design.