Abstract. Purpose. The subject of this study is the strength of the loaded units of mobile machines for flash butt welding by refining high-strength rails. The theme of the work is related to the development of a technique for strength calculating of the insulation of the central axis of these machines. The aim of the paper is to establish the mathematical dependence of the pressure on the insulation on the magnitude of deflections of the central axis under the action of the upset force. Design/methodology/approach. Using the Mohr's method, the displacements of the investigated sections of the central axis under the action of the upset force and the equivalent load distributed along the length of the insulation were calculated. The magnitude of the load distributed along the length of the insulation equivalent to the draft force was determined from the condition that the displacements of the same cross sections are equal under the action of this load and under the action of the upset force. Results. An analytical expression for establishing the relationship between the pressure acting on the insulation and the magnitude of the upset force and the geometric dimensions of the structural elements of the machine was obtained. Based on the condition of the strength of the insulation for crushing, an analytical expression for establishing the relationship between the length of insulation and the size of the upset force, the geometric dimensions of the structural elements of the machine, and the physical and mechanical properties of the insulation material was obtained.Originality/cost. The proposed methodology was tested in the calculation and design of the K1045 mobile rail welding machine, 4 of which is currently successfully used in the USA for welding rails in hard-to-reach places.