By analyzing the vibration process of cold rollilng and using the stru cture mdel of rolling system, a rolling force mathematical model was built. In t he model, the following factors are considered: roll and strip elastic deformati on, strip height, rolling tension, the length of contact arc, frictional state, rolling speed and so on. After substituting the force model into the vertical an d torsional vibration equations of motion of the rolling mill, a coupled set of equations is obtained, and the stability of the equations is analyzed by using t he Routh criterion. By use of simuation, the model is confirmed, and the influen ce of different working conditions and the coupling between vertical and torsion al vibrations on the stability of the vertical system of the mill is discussed, which builds up a ｆoundation for further study of the coupled vibration of roll ing mills．