Abstract: A dynamic model was developed with kinematic differential equation derived for a dual-disc over-hung rotor system with rub-impact fault. The stability of the system and stability regions were studied by setting up nonsingular linear transform matrix and by use of Jacobi matrix in combination with the theory of Routh Hurwitz. Then, the effects on the stability regions of the system were discussed with relevant parameters. The results showed that such a semi-analytical method is available to get the stability regions and their corresponding rotational speed and damping ratio. Simultaneously, it was found that the contact clearance and friction coefficient both affect the stability regions clearly, and the steady-state periodic solution can reflect the system response. The results as above will provide a theoretical reference for safe running in actual operation.