<p>Blades are the core component of energy conversion for turbomachinery, and reducing the blade-casing clearance contributes to improved engine efficiency. However, this is commonly accompanied by a high risk of blade-casing rub and induces severe rubbing deformation under the potential rotor misalignment factor, causing a geometric nonlinearity. In this paper, a dynamic model of a rotating pre-twisted blade, incorporating geometric nonlinearity, elastic boundary, and centrifugal effects, is proposed based on classical shallow shell and Von Karman nonlinear theories. Then, the motion equations of the rotating blade are obtained using Hamilton’s principle and a model function constructed with Chebyshev polynomials. Considering the rotor angle misalignment factor, a blade-casing rubbing force model is proposed that includes the point and linear rubbing along the chordwise direction of the blade. Both models are verified by a comparison with available results in the literature. Subsequently, based on the proposed model, rub-induced nonlinear vibrations of the blade under different rotor angle misalignment cases and casing stiffness are evaluated. The results show that intermittent full annular rubbing and local continuous rubbing would be induced under different rotor angle misalignment cases and casing stiffness. Blade-casing eccentric rubbing induced by rotor angle misalignment around the blade-thickness direction is more severe than misalignment around the spanwise direction. The response induced by the local continuous rubbing exhibits a strong nonlinear characteristic, and blade bending characteristics are more easily excited.</p>