Abstract <p>We consider plane contact problems with a limited contact area for elastic bodies with a regular microrelief (RMR) applied to their surfaces. It is assumed that Flamant’s solution to the problem of the action of a concentrated normal force on the boundary of an elastic half-plane can be used to determine the stress-strain state of bodies. When modeling the contact interaction, a calculation scheme was used in which one of the bodies is considered as a rigid punch, and the second is considered as an elastic half-plane with a composite modulus of elasticity. The single-parameter families of punches with RMR are considered, the parameter of which is the number of microprotrusions. The regularities of contact interaction of punches with RMR and elastic half-plane were investigated by the method of computational experiment. Based on the established patterns, a method for approximate calculation of load distribution between RMR elements, as well as assessment of contact pressure, sizes of actual contact areas and average final gaps on microprotrusions is proposed.</p>