A variable cross-section cantilever hollow cylinder is a special structure widely used in engineering. Based on the quasi-static limit analysis and impact dynamics, the dynamic characteristics of a cantilever hollow cylinder with a variable cross-section of constant thickness and variable thickness, under impact load, are studied respectively. The load position parameter and the plastic hinge position parameter are defined, and the conditions for determining the position of the plastic hinge are given based on the load position parameter. The expression of acceleration of the cantilever end and the control equation of the plastic hinge position parameter is derived from the momentum theorem and the moment of momentum theorem. According to the differential relationship between distributed inertial force and shear force and the differential relationship between shear force and bending moment, the expressions of shear force and bending moment are derived. The influence of the load position parameter on the plastic hinge position parameter and on the acceleration of the cantilever end, and the influence of the plastic hinge position parameter on the acceleration of the cantilever end are analyzed. The results of calculation examples show that when impact load obviously exceeds the static limit load of fixed end and the load position parameter μ is smaller than the critical load position parameter μic, the plastic hinge is located in the cylinder; the theoretical results of the acceleration of cantilever end ac and the plastic hinge position parameter λ are in good agreement with their numerical results; λ increases approximately linearly with μ; μ-ac relation curve and λ-ac relation curve are similar.