Abstract: The transverse buckling of a strip involves a serious flatness defect, and its mechanism of production is still unclear. Based on Airy stress function and Timoshenko's principle of least work, a new mechanical model of transverse pre-buckling is established, and the stress field in the strip prebuckling state is obtained. The mathematical model of the critical buckling stress is also built by Galerkin's principle of virtual displacement.The results of the analysis could be used for prediction of the transverse buckling in the annealing furnace.