The object of research is the hinge unit of the universal spindle of rolling mills. The most common for such conditions are used hinges with anti-friction liners with sliding friction. One of the most problematic parts of the hinge with sliding friction is the uneven distribution of pressure on the contact surface of the segments, which reduces the wear resistance of liners and operational reliability of the spindle. To identify the causes of uneven pressure and determine areas of significant excess of torsion loads, studies are carried out on the developed mathematical model of the hinge. In the course of the research, a mathematical analysis of the influence of the parameters of liners on the magnitude of pressure on the contact surfaces under the working loads of the roller blades and segments of the hinge liners is used. The parameters of the zones of high pressure in the contact liners typical forms in the form of a continuous segment with flat and cylindrical surfaces. It is established that it is necessary to change the liner section plane along the length and width of the segment. Analytical dependences of the hinge parameters on the active loads and pressure are obtained. The formulas for determining the geometric dimensions of the hinge segments with regard to its radius and rigidity are derived. The study of the hinge with inserts, in which bevels on a flat surface and slopes to the ends along the length and from the middle to the side faces, indicates the possibility of uniform distribution of pressure along the length and width of the segments of the inserts. Thus, research on the mathematical model and in the laboratory has shown that it is advisable to use the developed design of the liner with a variable section plane along the length and width of the liner. The uniform distribution of contact loads is confirmed by pressure plots along the length and width of the segments. This makes it possible to increase the wear resistance of the hinge joint of universal spindles of powerful rolling mills. Compared with the known designs of hinges, the operational reliability of the spindles and the period of trouble-free operation of states are significantly increased.