This paper investigates mechanical vibrations of an interior permanent magnet (IPM) synchronous electrical motor designed for a wide range of speeds by virtue of the modal and rotordynamic theory. Mechanical vibrations of the case study IPM motor components were detected and analyzed via numerical, analytical and experimental investigation. First, a finite element-based model of the stator assembly including windings was set up and validated with experimental and analytical results. Second, the influence of the presence of the motor housing on the natural frequencies of the stator and windings was investigated by virtue of numerical modal analysis. The experimental and numerical modal analyses were further carried out on the IPM rotor configuration. The results show that the natural frequencies of the IPM rotor increase due to the presence of the magnets. Finally, detailed numerical rotordynamic analysis was performed in order to investigate the most critical speeds of the IPM rotor with bearings. Based on the obtained results, the key parameters related to mechanical vibrations response phenomena, which are important when designing electrical motors with interior permanent magnets, are provided. The main findings reported here can be used for experimental and theoretical mechanical vibration analysis of other types of rotating electrical machines.