Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor. This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.