In engineering disciplines, both in scientific and practical applications, systems with a tremendous number of degrees of freedom occur. Hence, there is a need for reducing the computational effort in investigating these systems. If the system behaviour has to be calculated for many time instances and/or load scenarios, the need for efficient calculations further increases. Model order reduction is a common procedure in order to cope with such large systems. The aim of model order reduction is to reduce the (computational) effort in solving the given task while still keeping main features of the respective system. One approach of model order reduction uses the proper orthogonal decomposition. This approach is applied to Mikota’s vibration chain, a linear vibration chain with remarkable properties, where two cases of an undamped and a damped structure are investigated.