The influence of the low induced force is evidence in the ultra supercritical and the supercritical steam turbine. The dynamic characteristics of the flow induced force acting on rotor-seal systems is investigated in the paper.The nonlinear dynamic model of the rotor-seal system is established with Muszynska model. And Floquet theory is applied to study stabilities and dynamic behaviors of the periodic solutions in the systems. The dynamic characteristics of the system at the certain rotating speed and the certain physic parameters are analyzed by the periodical responses, Poincaré maps, frequency spectrums chart, bifurcation charts, etc.