Abstract: Internal damping is one of the most significant factors which can destroy the stability of the flexible rotorbearing system. The influence of internal damping on the flexible rotor system should be considered carefully when conducting such rotor design. With the increasing demand for these mechanical performance indexes, the influence of rotor internal damping on dynamic stability attracted much attention. It is of practical significance to structure design and performance improvement of highspeed rotating machinery to determine rotor instability speed or stability space of system parameters by analyzing internal damping of rotor. In this research, a typical rotorbearing system with internal damping was studied. There are two discs connected with a thin shaft and supported at its ends. In the modeling process, the linearization hypothesis was adopted, and all the supporting stiffness and damping in the model are linear. Both equivalent viscous damping dissipates energy equation and Lagrange method were adopted, so as to build the dynamic equations of the rotor system considering the internal damping. The above dissipated energy actually includes the energy dissipation caused by rotor rotation and revolution. When the rotational speed is low, the internal damping dissipation energy is mainly caused by revolution movement, while when the rotational speed is high, the energy dissipation caused by rotation movement is the main factor. The equations built in this research is composed of a set of terms which are respectively mass matrix term, stiffness matrix term, damping matrix term and forcing matrix term. A kind of numerical method was adopted to get the result of the stability by solving the equations. The result of the stability was mainly evaluated by the modal frequency which is expressed in complex form. The real part represents modal damping and the imaginary part represents modal frequency. The stability of rotor support system under different internal damping coefficients levels and different speeds was systematically analyzed. Due to gyro effect, each vibration mode was subdivided into positive precession and reverse precession. The mode frequency of positive precession increases with the increase of rotational speed, and the mode frequency of reverse precession decreases with the increase of rotational speed. The influence of the internal damping was discussed. The influence law of damping on the stability of rotating subsystem in different speed stages was given. The results show that when the rotor exceeds the critical speed, the internal damping will deteriorate the rotor stability. At the same time, the greater the internal damping value is, the lower the instability speed of the rotor will get. This research provides a convenient method for the calculation of internal damping.