The thin-walled casing and squeeze film damper (SFD) of an aero-engine have significant effects on the vibration of the rotor during maneuvering flight. However, few studies have been conducted on the vibration responses of a rotor-damper-casing coupling system under this condition. This paper uses Lagrange's principle to derive the equation of motion for a rotor system that considers the flexible casing and static eccentricity of the SFDs during maneuvering flight. The model of a casing is established, and the frequency response functions (FRFs) with pre-stress are calculated by converting the flight parameters to pre-stress. Then, the FRFs are generated for various flight statuses and combined with the rotor finite element model using the linear interpolation method. The vibrations of a dual-rotor system during the diving-climbing maneuver are calculated by the Hilber-Hughes-Taylor-α (HHT-α) method. The results indicate that the deflection will appear in the rotor vibrations during maneuvering flight. The flexible supports of a casing make the vibration transfer between the High Pressure and Low Pressure rotors, and there are harmonic and subharmonic components in the vibrations of a rotor-damper-casing coupling system. Due to the influence of a flexible casing, the vibrations of a rotor vary at different speeds under the diving-climbing maneuver, even if the speed is far from the critical speed. This study illustrates the significance of considering the flexible casing and the SFD during maneuvering flight.