The emitted noise of an exhaust system is divided into three different kinds of noise: Tailpipe noise, noise transmitted through the hanger into the cabin and surface radiated noise. This paper deals with the surface radiated noise which becomes more and more unmasked as the radiated sound power of other sources, e.g. of the tailpipe, decreases. Noise sources, the transfer path and the radiation of a structure are presented. A method for calculating and optimizing a structure with FEA (finite element analysis) is also part of this paper.An exhaust system is a complex dynamical system. Global eigenfrequencies of a whole exhaust system are below 200 Hz. A muffler moves then in rigid body motion and the radiated sound power is subjective not relevant. The main sound power is transferred through the hanger to the underbody. At higher frequencies the acoustical effects appear more local and are more effective in noise radiation. It is then possible to divide the exhaust system into small sub-systems and to calculate these separately from the surroundings. This means less computational resources and less modeling effort.The aim of this acoustical development work is to decrease the surface velocity of the exhaust components. This can be achieved by decreasing the excitation, by increasing the stiffness or by adding damping or insulation.The main factors influencing the structural velocity will be presented for standard geometric exhaust components. This means the influence of excitation, shell geometry, tube geometry, temperature and material. Geometries for modern exhaust systems, however, are becoming more and more complex. In order to place as much inner volume as possible in the underbody of a car, flat clamped shell mufflers with low eigenfrequencies are often used. In this case the use of a topography optimization tool like OptiStruct® from Altair Engineering® is required. Typical designs will be shown in this paper.