Apparatus for mechanical mixing of liquid-phase products are an integral part of technological lines of various industries. The reliability of this kind of technological equipment is largely determined by the dynamic stability of its operation, since a large number of factors affect the dynamic loading of mechanical systems (geometric features of mechanical agitators, moments of resistance, the design of drives and their links, rheological features of mixed liquid-phase products, the accuracy of assembly and installation, and much more). This research is devoted to the calculation of vibration resistance of the cantilever shaft of the apparatus for mechanical mixing of liquid-phase products subject to torsional vibrations. The contains the main provisions, the drive scheme of a mechanical mixer with a cantilever shaft and the development of a block diagram, as well as a dynamic transmission model of the drive of the apparatus for mechanical mixing of liquid-phase products. Also this work is devoted to obtaining and analyzing the amplitude-frequency and phase-frequency characteristics of the links (sections) of the model of the dynamic drive system of the apparatus for mechanical mixing of liquid-phase products without taking into account damping. Also of the research is devoted to the calculation of the shapes and frequencies of vibrations of a multi-mass drive system of a mechanical mixer with a cantilever shaft and their analysis (excluding damping) is performed.