A coupling dynamic model of a rotating cantilever beam is established by considering the effect of steady-state axial deformation on transverse bending deformation. The present method uses fully nonlinear Green strain–displacement relationship to derive the coupling terms in the equations of motion. The steady-state axial deformation is derived by analysing the equation of axial motion. An expression of the rotational speed limit is also obtained. The numerical results indicate that the steady-state axial deformation has a considerable effect on the transverse bending frequencies. A comparison of the present model with the absolute nodal coordinate formulation indicates that the two models are in good agreement, which proves the effectiveness and rationality of the present model.