In this paper, the rubber bearing/shaft system is simplified into a nonlinear elastic bearing/shaft system. A general bearing/shaft rubbing system with nonlinear elastic support of stator is established and is analyzed by the modern nonlinear dynamics and bifurcation theories. The boundaries for the existence of the no-rub responses are determined analytically, and the synchronous full annular rub solution are derived and the stability is analyzed to determine the region of the synchronous full annular rub response. The results provide an opportunity for a better understanding of the dynamical characteristics, such as the synchronous full annular rub motion, the jump phenomena as well as the transition between the full annular periodic rub motion and the unstable rub motions. A systematic study on the influence of the system parameters such as damping and eccentricity on the dynamics characteristics is carried out. An overall picture of the response characteristics of this model is then obtained by drawing the existence boundaries in the parameter space. The present results provide good understanding on the relationship between the different rubbing responses and the system parameters.