The basics of the design of rotary kilns, widely used in the processing and preparation of various raw materials, are described. It is shown that the weak point of the rotary kilns design is the support rollers, which carry the entire load of the kiln and are initially made of less durable steel than a bandage being in contact with them. In fact, the design itself provides for the possibility of periodic replacement of the «miscellaneous part», which is a support roller. However, for an operator, any downtime of equipment leads to economic losses. Therefore, the goal has been formulated: to increase the durability of the support rollers avoiding a significant change in the kiln design. For this purpose, initially, from the point of view of contact mechanics, the basics of the interaction of the surfaces of the support roller and the bandage of a rotary kiln have been studied. Calculation models for various contact options of these parts have been given. The force model of contact between the surfaces of the support roller and the bandage has been studied. The maximum normal and tangential stresses in the contact zone, at its boundary and beyond have been determined. At the same time, complex processes occur in the contact area of the roller and the bandage surfaces, in particular, micro-slipping and sliding, due to the difference in the diameters of the rotating bodies and the difference in the level of their mechanical properties. Micro-slip is one of the sources of fretting wear. However, the most significant wear occurs as a result of mechanical interaction and changes in the structure of the surface layer with the gradual accumulation of various kinds of defects in the crystalline structure caused by plastic deformation of the surface layer of the contacting parts. It is shown that not only the mechanical and operational properties of the material for their construction, but also the displacement of the contact spot during kiln operation have a significant effect on the wear process of the support rollers. The displacement can be angular or linear, and in real conditions it is most often combined, it is caused by the thermal expansion / compression of the metal structure and the operating conditions of the rotary kiln.