<p>This study has investigated the buckling modes of the freight cars subjected to tensile longitudinal forces. The relevance of this research lies in the necessity to derive analytical relationships that assess the impact of such forces on both the buckling behavior of railcars and the resistance of wheelsets to derailment caused by the flange climbing onto the railhead during operation. In the course of theoretical analysis, the differential equation of bending has been derived along with expressions based on the displacement method and the response of tension–bent rods to unit displacements and loads. The developed approach contributes to enhancing the resistance of railcars against flange climb derailments under traction operating conditions.</p>