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The article presents accurate solutions for the problem for two elastic half‐spaces with an arbitrary curvilinear interface. Our study shows that dilatation solutions (Poisson integrals) are dependent on neither an overall compression modulus nor the Poisson ratio, and depend only on the velocity of longitudinal waves. These specific solutions can be supplemented by general solutions for an incompressible elastic medium, and the boundary conditions of the rigid contact for the sum of thedoi:10.5800/gt-2019-10-2-0422 fatcat:mvucwuj7vzfg5hj5pidkpvg5ve