Low-temperature cracking is one of the main reasons for the deterioration of the upper layer of roads in regions with cold climate. The material of the top layer can be, e.g., asphalt concrete or frozen soil. In this paper it is assumed that the temperature of the underlying layer is non- negative, i.e. a model in the form of a two-layer structure is used. A large number of works aimed at preventing wear are known, but the interdisciplinary problem of low-temperature cracking in seasonal freezing of soils remains relevant. In publications, as a rule, consider the destruction of freezing, that is, with a decrease in temperature. Much less attention is paid to the modeling and forecasting of damage to the upper layer of roads, if its temperature rises, but remains negative. In this case, the layer is compressed and the appearance of wave-like irregularities on the day surface (buckling) is possible. The objective of the current study was modeling the conditions of occurrence and prediction of damage to the upper layer of roads when the changes negative temperature. The paper uses methods of mathematical modeling of mechanical systems, as well as adaptation of the known results of other authors. The estimation of the critical wavelength at a bend of the compressed upper layer is given. The results of numerical simulation are consistent with the experimental data known in the literature.