The real-time monitoring of rotors is used to speed up the identification of damage and allows to reduce the risk of failures. The detected vibration signal needs algorithms to be analysed and classified, moreover require an accurate placement of sensors. It is also possible to create a digital replica of the physical systems to simulate the behaviour of the machine and to carry out all the necessary tests. Vibration monitoring analysis offers lots of information about anomalies that could be present inside rotating machines. These usually generate inside bearings which are critical elements for the safety of the entire system. The work of this master’s degree thesis focuses on the creation of an analytical-numerical model to describe the behaviour of a flexible rotor supported by rolling elements bearings.