In last time, vibrations analysis and monitoring are become the most widespread and softest part of machines diagnostics. Detection, identification and removing of problems about work of machine is simpler if we modeling few dynamics solution. When forming model which oriented on discovering defect by means sensors measured vibrations, which almost located in bearings, mathematics model is presented as elastic rotor with concentrated weight. As note, mathematics model in the most cases based on radial oscillation of rotor and torsion oscillations in someone cases. Torsional vibrations are not detected without special sensors even if they are his magnitude near destruction level. This paper presents one of the ways of modeling rotary machines, which is oriented towards the identification of the causes of problems in their operation. These mathematical models are the result of experimental research by some of the world's leading companies. The importance of these models in detecting damage was confirmed during testing on real machines during exploitation.