Higher parameters of centrifugal machines are constantly required, such as the pressure of the medium to be sealed and the speed of rotation of the shaft. However, as the parameters increase, it becomes more and more difficult to ensure the effectiveness of sealing. In addition, sealing systems affect the overall safety of equipment operation, especially vibration. Non-contact seals are considered as hydrostatic-dynamic bearings that can effectively dampen rotor oscillations. Models of “rotor-gap seals” system and impulse seals have been studied to assess the effect of these seal systems on the oscillatory characteristics of the rotor. Analytical dependencies are obtained for calculating the dynamic characteristics and stability limits of seals as hydromechanical systems. The proposed general technique makes it possible to purposefully select the design parameters of seals to adjust sealing systems to work in vibration-safe modes due to a targeted increase in the rigidity of non-contact seals are determined. It leads to an increase in the vibration resistance of the centrifugal machine’s rotor. Comparison of the results of calculations of frequency characteristics according to the obtained expressions with the data of experimental studies showed that the calculation errors do not exceed 5%, which allows using for practice the obtained dependencies in the calculation and design of centrifugal machines sealing systems with sufficient accuracy.