The dynamics of rotating machinery have been extensively investigated during the past century. To date, longer rotating shafts, higher rotating velocity, higher fluid pressure, and generally high performances are required. For this purpose, a deep understanding and a more accurate modelling of the rotating machinery dynamical behaviour is needed, especially in terms of the resultant vibrations and stability issues. In this paper, a mathematical model was developed for a simple rigid rotor-bearing system using finite element method. Several natural frequencies and corresponding mode shapes of the systems were presented. In order to validate the model, some experimental tests were performed using a small test rig. The response of the system in the frequency domain and the direct orbit of the shaft were plotted as well.