Purpose: The issues of securing wheeled vehicles on a universal railway platform are considered. In practice, the most common method is securing tie-downs around the axles of the wheeled vehicles. A study has been conducted to determine the optimal parameters of wire tie-downs depending on their placement on the freight. The conducted computational experiment has revealed that the applied place of fixing the tie-downs is not optimal. The influence of various factors on the number of nails for fixing the bumping posts securing the wheeled equipment has also been investigated. Methods: The theory of planning a multifactorial experiment, methods of regression analysis are applied. Results: The influence of the geometric parameters of the placement of tie-downs on their bearing capacity has been established, provided that the wheeled equipment is secured from rolling. Practical significance: The obtained research results allow us to choose the most rational points for fixing tie-downs on the frame of wheeled vehicles and the platform. The proposed method has been tested during the transportation of wheeled vehicles from the stations of the Oktyabrskaya Railway branch of JSC “Russian Railways”.