In widespread sources the results of calculations of the sizes of contact planes of anellipse form at interaction of locomotive wheels with rails of type P65 which small axes make 5-10mm depending on loading taking into account dynamic influence are resulted. These data do notcorrespond to the purpose and objectives of this study, which is to determine the size of the half-axisof the contact plane under vertical load on the head of the rail thread in the range from 100 kN to180 kN, when the wheel of the freight car rests on a bevel a wheel having a conicity of 1:10, with awheel radius r1 = 475 mm and a rolling surface radius of the rail head r2 = 80 mm. The size of thecontact plane of support of the rim of the wheel of a freight car on the surface of the head of the railtype P65 is determined in the work. The calculations were performed on the basis of preliminarydetermination of the location of the mathematical point of contact on the box curve, which outlinesthe surface of the rail head in cross section under deterministic conditions of pressing intermediaterail fasteners of separate type under the action of outstanding accelerations for freight -0.3 m / s2.The purpose of the calculations is to obtain the practical value of the maximum dangerous width ofthe rail track, which corresponds to the conditions of track expansion at vertical wheel load on therail 140 kN and at maximum spacing forces that provide the highest values of lateral displacementsrail thread with a surface adjacent to the chamfer of the wheel rim. Based on calculations by the Hertz-Bilyaev method, it was obtained that the average value of the contact strip of the rail and therim of the wheel of a freight car, at a vertical load P = 140 kN, is: b = 3.2 mm, so b / 2 = 1.6 mm.But if you round to the accuracy of measuring the width of the rail track - b / 2 = 1.6 mm.