The object of the research is pile-soil interaction under freezing and frost heaving. Modeling of pile-soil interaction on the basis of joint solution of static equilibrium equations, physical equations for stresses and equation of thermal conductivity is considered. No such solutions have been found in existing publications. In this study, a model of pile-soil interaction in the form of a closed analytical solution with respect to the pile geometry was developed. Methods of continuum mechanics and elasticity theory were used. The model was a mathematical record of the equilibrium of forces acting on the pile. It was reduced to second-order algebraic equations with respect to its geometric parameters. The static equations of force equilibrium written in quadratic form related the geometric parameters of the pile to the stress-strain state and the thermal characteristics of the soil. Physical equations for heaving stresses and the thermal conductivity equation closed the problem. The model was developed as applied to a pile with an upper reverse taper. It reflected the performance of the pile during freezing and frost heaving and allowed determining its required geometric parameters under the given soil and climatic conditions.