A sudden loss of lateral stability (strip track-off) is a serious operational problem in cold rolling of steel that often leads to catastrophic consequences such as mill crashes and roll damage. This paper studies the causes of instability in lateral motion of a metal strip in a single span between the uncoiler and the first stand of a cold rolling mill. A mathematical model of strip lateral dynamics that includes a rolling mill model and a simplified physically based model of strip buckling is formulated. The numerical analysis of the model reveals that in the presence of strip buckling, the lateral motion becomes unstable once a critical level of asymmetry in rolling conditions is exceeded. The critical level of asymmetry increases with the increase in the tension applied to the strip. Below this critical level of asymmetry, a sudden transition to unstable motion occurs if a critical lateral deviation is reached. This paper demonstrates that the buckling of the strip can be responsible for lateral instability. The results of this paper explain the sudden onset of instability observed in metal rolling and the stabilizing effect of the tension applied to the strip, known in rolling practice.