The object of the study in this work is the relationship between the elastic modulus, tensile stresses and deformations of frozen sandy soil with evolving cracks using the example of three-point bending. The goal is to develop a methodology for determining the modulus of elasticity and tensile stresses in frozen sandy soil under force indirectly. The choice of the object and the purpose of the study is motivated by the relevance of the soil strength problems during seasonal freezing. To achieve the goal, methods of mathematical modeling of mechanical systems with changing characteristics during the deformation, also the testing methods of samples on the SHIMADZU AGS-X test machine were used. A mathematical model has been developed, the realism of which is ensured by taking into account the evolution of a crack and using the effective geometric characteristics known from fracture mechanics. It has been substantiated that the destruction of the material occurs on the descending branch of the «load - displacement» diagram. The simulation results are consistent with the data known in the scientific literature. The condition for the model application is the existence of an extremum point on the curve «load - displacement». Prospects for the development of the topic are associated with the adaptation of the proposed approach to the analysis of the of frozen soil state, taking into account its rheological properties.