This study is devoted to study of most used existing models of contact two solids, in relation solution of problem dynamic interaction of wheel pair and the rails. In paper also proposed and approbate a new relationship to connect force of interaction, deformation of local indentation, displacement of contacting bodies, their mechanical and geometric characteristics, as well as the parameters of condition during operation in different modes. The stress isolines at point of interaction wheel-rail on straight section of track without taking into account the defects of the contacting bodies are obtained.