In this study, the dynamic behavior of a hollow cylinder under a periodic, consecutive moving force applied at the inner hole is investigated. The cylinder is assumed to deform large compared to the classical linear elastic material, so that the Neo-Hookean constitutive model is employed. The cylinder is fixed at the top and bottom surfaces in the present model. The resulting governing equation and the associated boundary conditions appear to be highly nonlinear in the cylinder’ s displacements. After performing the eigen analysis on the present system, an appropriate biorthogonality condition is obtained. Galerkin’ s method is applied, in conjunction with the eigen analysis results, to obtain the discretized equation of motion, which include the nonlinearity of both the governing field equation and boundary conditions. As a result of the successive nonlinear analysis, the cricical speed of the moving force could be derived and the influences of the nonlinearty on the dynamic behavior of the cylinder are examined. with the eigen analysis results, to obtain the discretized equation of motion, which include the nonlinearity of both the governing field equation and boundary conditions. As a result of the successive nonlinear analysis, the critical speed of the moving force could be derived and the influences of the nonlinearty on the dynamic behavior of the cylinder are examined.