This paper is concerned with chatter in tandem cold rolling mills, which has been recognised to have close relation with friction conditions in roll bites. However, the relation between rolling conditions and the stability of vibration has not been clearly understood. Therefore, an attempt is made to understand how the rolling conditions can be related with vibration phenomena, through numerical simulations.Firstly, a theoretical model is constituted to simulate the vibrational behaviour of a five-stand continuous rolling mill, and the stability of the mill vibration is evaluated, introducing a disturbance to the static rolling conditions. The results of the calculation show that the vibration is greatly influenced by rolling speed and friction coefficient. With increase in rolling speed, the mill vibration tends to be self-excited. Also, the results show that optimal range of friction coefficient exists in which the vibration is damped and the mill is stable against the disturbance.Secondly, a simple self-exited vibration model is proposed and the stability index is proposed for further understanding of the phenomena. An analytical approach is made to predict the stability of the rolling process. With this model, it is shown that the rolling force and the delay of the response to the change in gap have a major effect on self-exited vibration. Also, the calculated optimal range of friction coefficient in the continuous rolling simulation can be explained by using the analytical model.