Consider the lateral dynamics of a strip between the uncoiler and the first stand of a cold rolling mill: operational problems are experienced in the metal rolling industry. Here we introduce a physically based model for the buckling of the strip between the uncoiler and the reduction mill. The model reveals, for the first time, that there exists a critical level of asymmetry in rolling conditions above which the strip motion becomes unstable. Below this level, two solutions of the steady-state model exist. Whereas one of these solutions represents a stable equilibrium, the other exhibits the features of unstable equilibrium. The motion of the strip is sensitive to the initial lateral deviation of the strip. For a given level of asymmetry, a sudden transition to unstable motion occurs if a critical lateral deviation is reached. The model can be used as a basis for development of a multi-stand model of lateral dynamics.