Blade-casing contact is one of the common forms of failure in aero-engines, and the system nonlinearity introduced by rubbing greatly increases the rotor vibration amplitude and the difficulty of motion prediction. Most of the existing studies on rotor nonlinear friction are simplified to the contact between a rigid disk and a circular casing, ignoring the form of blade-casing contact and the flexibility of the shaft. In view of the above problems, this paper establishes a flexible rotor model considering the contact of multi-blade and casing, compares the rotor model with the finite element model to verify its accuracy. In addition, the effects of different eccentricity and number of blades on the amplitude-frequency curves and bifurcation of the rotor system are investigated. The results show that the rubbing failure introduces strong nonlinearity to the rotor system, which makes the amplitude-frequency curves show hard characteristics, and the rightward deviation of the amplitude-frequency curves becomes more obvious with the increase of the degree of rubbing. In addition, the number of blades also has a greater influence on the nonlinearity of the rotor. The model can provide a reference for the vibration analysis and motion prediction of rotating machinery with rubbing faults.