The dynamics of the vibration machine with unbalance vibration exciter taking into account the elasticity of its connection with the asynchronous motor is studied. The expression describing torsional oscillations of the elastic coupling in the steady (near-steady) operation of the vibration machine and the formula of the vibratory moment for the machine with plane oscillations of the working body are obtained. The amplitude-frequency characteristics of oscillations of the vibration machine drive using “soft” and “rigid” elastic couplings are constructed. It is shown that resonant oscillations can arise in the vibration machine drive. The nature of changes in the magnitude of the vibratory moment (additional dynamic load on the motor caused by oscillations of both the bearing body of the vibration machine and the elastic coupling), depending on the vibration exciter speed is determined. It is shown that the presence of the elastic coupling in the vibration machine drive in certain operation modes can lead to an increase in the motor load and promotes the appearance of the Sommerfeld effect during start-up. Critical frequencies of the vibration machine drive with unbalance vibration exciter are specified. Recommendations on the choice of natural frequencies of the drive in order to avoid resonant oscillations are formulated. By means of computer simulation, the emergence of resonant torsional oscillations of the vibration machine drive during the passage of the natural frequency region and the associated manifestation of the Sommerfeld effect are demonstrated. The effectiveness of the proposed recommendations for reducing drive oscillations is confirmed. The results obtained will allow avoiding resonant oscillations in the vibration machine drive, thereby reducing the dynamic loads in the elements of its design and increasing the reliability and durability of the drive parts