According to the lumped mass method, the drive system of rolling mill can be simplified as a three-degree-of-freedom spring-mass model. The nonlinear dynamics equations are established considering nonlinear torsion stiffness of connecting shaft and nonlinear friction force between roller and strip, and Hopf bifurcation and critical parameters are analyzed by applying the Hurwitz algorithm criterion. Furthermore, the system stability is numerically simulated through time-history and phase plots. The results indicate that the system motion can be stable in some range of parameters, and the bifurcation phenomenon occurs and the stability may be lost across the critical points. In addition, at different bifurcation points the phase orbit run along diverse skeleton curves of revolution. These conclusions are significant to reveal the mechanism of system bifurcation and stability, and help for optimization of technology condition in practical application.