A significant share of structures includes the components that are in contact with each other. These include, for example, stamps, molds, machine tools, technological equipment, engines, etc. They are characterized by a varied load mode. Therefore, an important aspect in studying the stressed-strained state of such structures is to determine the dependence of contact pressure on the external forces applied to them. A superposition principle for contact problems is not applicable in a general case. However, for this type of structures, the linear dependence of contact pressure on the load level has been established. In this case, the contact area does not depend on the load level. It has been demonstrated that this pattern holds not only for a one-component but also for the multi-component load. As a result, the possibility for rapid determining the stressed-strained state of such structures is ensured, while maintaining the accuracy of the results obtained.The applicability of the constructed method has been demonstrated by using the machine tools’ clamping accessories as an example. The established patterns are important when estimating the designs of structures. The derived direct proportional dependence of the solution on the applied loads makes it possible to shorten the design time of structures with the elements that interact when they are in contact at surfaces of the matching shape. In this case, we have considered different sets of loads, as well as the various varying variants of these loads. The examined cases have confirmed the direct proportionality of the components of the stressed-strained state of the magnitude of the applied forces for the case of their coordinated change. It has been also shown under an uneven change in the individual components of loads the dependence of contact pressure and components of the stressed-strained state of the examined objects on the applied forces demonstrates a complex character different from the directly proportional relation. The established dependences underlie the substantiation of the design and technological parameters of the structures that are designed, as well as their operational modes