The energy dissipation in assembled metal structures is mainly related to various physical phenomena – usually modelled as dry friction – on the contact surfaces. However, the reliable numerical modelling of assemblies is a challenging task due to the complexity of the contact mechanisms. To fit the models to experimental results, it is beneficial if the material damping can be separated from the contact damping. The paper presents measurement results aiming to distinguish material damping from the damping related to the contact between the conforming surfaces of assembled machine parts. To evaluate the role of contact in damping and to find a connection between the contact-related increase of modal damping and the mode shapes, the modal damping ratios of a monolithic body and a shrink-fitted assembly are compared. It is demonstrated that the contact damping is linear in the examined case. Based on the experiments, a finite element (FE) model was developed that does not apply computationally expensive contact algorithms. The FE model was able to reproduce the measured modal damping values of the assembled structure at all the natural frequencies that fell in the frequency range of the measurement. This result is achieved by fitting only a single damping parameter. The research work is motivated by metal cutting, where the damping of the machine-tool-workpiece loop plays a key role in the stability of the process, particularly in case of high speed machining.