Unbalance of rotating components is a highly destructive phenomenon that adversely affects the operation of a machine. Unfortunately, there are no instruments that allow unbalance to be detected directly during machine operation, which makes it necessary to monitor the secondary effects of unbalance. An additional factor that complicates the detection of unbalance is the coupling of the motor with the driven machine. The method of connecting the two machines is also significant. The article discusses selected methods for detecting rotor unbalance in single – mass and two – mass systems with elastic coupling. The adopted mathematical models based on gravitational force and centrifugal force are presented. The laboratory test stand and research methodology are also described. To model the unbalance, a test mass is added to the disc rotating on the motor shaft. The added mass constituted less than 0.5% of the mass of the rotating components. Tests were conducted in steady-state conditions at a speed below 20% of the motor’s rated speed. The study analysed mechanical vibrations and the reference current from the control system. Fast Fourier transform and higher-order bispectrum analysis were used to obtain diagnostic symptoms.