Chatter is one of the major problems in the cold rolling of strip in tandem mills. Reduction in productivity due to chatter vibration has important consequences on the price of rolled strips. So chatter is not only an industrial problem, but also an economic concern in modern rolling mills. Thus, capability in controlling the chatter phenomenon seems necessary. The present research can be divided into two main parts. In the first part, the major mechanisms of chatter are identified and this phenomenon is modeled based on the simple friction models using the MATLAB and SIMULINK softwares. As well as adding supplementary cases such as the nonlinear solution of rolling process model, considering the effects of the material strain-hardening and the elastic deformation of the work roll, the model relaxes certain assumptions. The simulation results which are: critical speed, dominant frequency, rolling force and torque are compared to the experimental data obtained from Mobarakeh Steel Company. Many experimental investigations have led to the point that friction is one of the effective factors causing chatter. A numerical method is developed to introduce a relationship between the Tresca friction factor and the Coulomb friction coefficient. A parametric study on the effects of friction coefficients of the two stand rolling mill on the chatter critical speed is conducted. One of the most important achievements of the first part is that an optimal setting of friction coefficients improves the process efficiency. Under the operating conditions stated in this study, the friction coefficient of the second stand should be increased as much as possible in order to get closer to its optimum point. The optimum friction coefficient of the first stand, however, depends on the friction coefficient of the second stand. The structural vibration of machines results in unsteady lubrication regime and thus friction is time and position dependent. A thorough understanding of unsteady lubrication phenomena can help to build a more realistic friction model for the unsteady processes, or to devise an operating strategy to avoid vibration. Therefore, in the second part of th is dissertation a new chatter model of the cold strip rolling with consideration of unsteady lubrication is proposed. The model is extended to the mixed lubrication regime by taking the surface roughness interactions between strip and work roll surfaces into account. Also, the results of this part are compared to the results of first part and verified using the experimental data from the viewpoint of the four output parameters. Effects of major parameters of rolling lubricant on the chatter critical speed are examined. The results of second part indicate that by considering unsteady lubrication the chatter model is more accurate, and also under the operating conditions of this study the limiting shear stress is an effective parameter. The main innovations of this research are: determining effects of friction on chatter in tandem mills, modeling the chatter phenomenon in the cold strip rolling with consideration of unsteady lubrication, and evaluating effects of major lubricant parameters on the chatter critical speed using the simulation program. Key Words: Cold Rolling - Vibration - Chatter - Friction