SUMMARY
Rails –are the basic constructive element of the top structure of a railway which directly perceive dynamic loading from a rolling stock. During their operation in rail metal there are the irreversible processes lowering their carrying capacity. Thus carrying capacity of rails is provided under the conditions that working loading for all period of their operation should not exceed admitted probabilities. The developed mathematical model takes into account casual rails load process load rails and carrying capacity, and also non-stationary character of reduction strength properties of rails. It allows to investigate all range of operational work of rails in a track at the given strength.