Objective: study of the stress-strain state of the wheel pair of a freight car in the process braking. Methods: to determine the stress-strain state of the wheel pairs of a freight car. Results: A volumetric finite element model of a wheel pair with rail sections was created using a finite element of the ten knot tetrahedron type, and maximum shear stresses and maximum equivalent stresses were determined according to the Mises and Dang Wan theory. Practical significance: It is shown that the maximum tangential stresses are observed at a point located at a depth of 4.5-5.3 mm below the rolling surface of the wheel. In case of emergency (short) braking, maximum stresses occur on the rolling surface of the wheel. During prolonged braking (movement of the train along a prolonged descent), maximum stresses occur at the point of transition from the disk to the rim on the inner side of the wheel, and the magnitude of these stresses is 2.5 times higher than in the emergency braking mode.