The problems of non-stationary heat conductivity with phase transitions, associated with soil freezing, are solved by enthalpy methods; the history of development of the method for the generalized problem of Stefan is presented. An algorithm of calculations of the processes of solidification-melting in moist soils, based on the explicit finite difference approximation of enthalpy equation, being the function of temperature and iciness is proposed. A graphical expression of solutions for different zones of a phase transition in large-dispersed and fine dispersed soils is presented. On the basis of the proposed algorithm a series of programs in different programming languages was developed, as well as the version of criterion form of solution, and by processing of a large number of numerical experiments, by the method of similarity "a generalized method of calculations of seasonal cooling device" has been created.