For many technical applications it is necessary to avoid or to reduce vibrations. Factors benefiting from vibration reduction are for example the durability of the application, which is increased, as well as cost expenses and the level of noise, which are both decreased. Rough, bolted interfaces are common in most machines and can be used as damping devices with some effort. Perhaps in future such contact surfaces could be used as damping devices at the interfaces of an automotive engine or exhaust system. Nevertheless it is difficult to predict the effect of a change in contact interface parameters on the dynamic behavior of the entire mechanical system. Therefore a method for calculating the steady state behavior of elastic multi-body systems was developed. The basis of this method is a finite element model of each contacting unit. On each model a modal reduction is applied in order to reduce the degrees of freedom. The method of Ritz and Galerkin is used to calculate the frequency response functions of the reduced system including contact. This method allows the calculation of the steady-state behavior of elastic multi-body systems with rough, bolted contact interfaces, by taking the pre-stress of the bolts, the roughness and the friction coefficient of the contacting surfaces as parameters. In order to verify calculated results, a test stand was built. The comparison of calculated and experimental results showed a satisfying correlation.