Abstract: The periodic time-varying equations for motion of the coupled rotor/fuselage system are formulated by building a new 24DOF coupled rigid/elastic element which includes 15 nodal deformation from the finite element discretization,3 rigid rotation of the flap,lag and pitch motion and 6 elastic deformation of the hub.Then they can analyze the elasticity of shaft and fuselage of helicopters by the finite element method.The dynamic coupling effects between the rigid motion of blades about the flap,lag and pitch hinges and moderately large elastic deflections are taken into account.After deriving linearized perturbation equations about the known equilibrium position,the stability is studied with the Floquet theory.Results show that the sectional stiffness of the shaft has a considerable effect on the stability of the coupled rotor/fuselage system.