In order to ensure high technical characteristics of machines for various applications, it is necessary to increase the strength of the most loaded and heavy-duty elements of constructions, which are complex-shaped components under intense contact loads. When bodies get in contact over surfaces of close shape, new factors that have not been taken into account before come into play. In particular, nonlinear contact stiffness of the surface layers of the components is among them. Accordingly, nonlinear components appear in impenetration contact conditions instead of traditional linear ones. To study the contact interaction with account for such constraints, a new method for stress-strain state analysis and structural strength design of various machine parts has been developed on the basis of a modification of the Kalker’s variational principle. Nonlinear models of the material behavior of the surface layers of contacting complex-shaped bodies were created and applied. The discretization of the resulting mathematical problem was performed with the help of the developed version of the boundary element method. The developed models of contact interaction combine physical and structural nonlinearities. This provides more accurate modelling of stress-strain state of contacting complex-shaped bodies in comparison with conventional approaches. The peculiar variation of the contact pressure distribution with the change of the gap shape and the properties of the interface layer between the contacting bodies were studied on this basis. It is possible to derive more relevant recommendations to justify design and technological solutions with account for the results of such analysis. Eventually, this will enhance the technical characteristics of machines of various applications