The object of the study is the soil susceptible to cryogenic cracking during freezing. The formation of cracks creates the problems in the development of mineral deposits in northern regions with sharply continental climates in Europe, Asia and North America. The destructive effects of cracks on the construction of roads and linear structures require the prediction of cryogenic cracks. The developed mathematical model and the method of its use provide the prediction of the processes of frost cracks formation in harsh climates. The calculation algorithm realizes the procedures for the step-by-step solution of the spatial strength problem for a fragment of a soil mass taking into account changes in temperature fields and physical and mechanical properties of frozen soils over time. The given example demonstrates the results of predicting of cryogenic cracking of the soil in the form of graphs of stress distribution in the freezing massif. The calculation results illustrate the ability to predict the formation of frost cracks, the ability to determine the main parameters and periods of cracking. The research results can be used in the design of objects in the conditions of propagation of soils subjected to cracking.