Features of modeling of rotor dynamic parameters with the use of structural and constructive damping (taking into account the change in the coefficients of stiffness, damping in supports and damping in the material of the rotor) are considered. The translation, deformation and mixed forms of rotor oscillations are considered. The influence of the interaction of the damping properties of the rotor elements on the dynamic of the rotor are analyzed. The results are presented in the form of amplitude-frequency characteristics and orbit trajectories of movement nodes of the rotor axis at different parameters. The questions of construction of different models for calculations and analysis of dynamic behavior of rotors of the gas-pumping unit, taking into account damping characteristics of the rotor and supporting elements are considered. Investigation of the damping characteristics of rotor systems was carried out during their design with the help of mathematical modeling, which allowed us to determine by calculation the influence of the applied material and design features on the dynamic characteristics of the rotor system as a whole. The use of the beam-mass model allows to obtain bending and longitudinal forms of the proper oscillations and their frequencies, to perform a refinement analysis of critical velocities using the Campbell diagram, which allows to take into account the dependence of the frequencies of the proper oscillations and critical velocities on the speed of rotation, to conduct a forced oscillation analysis (for example, amplitude- frequency characteristics and trajectory of the rotor nodes movement), as well as the ability to take into account different models of resistance forces.