In this paper three fundamental contact problems in Rock Mechanics are revisited. The first problem pertains to the interaction of a thin liner with a circular opening in an elastic medium. The innovation of the proposed solution lies in the fact that the elastic ring is assumed to behave like a thin shell. It is shown that the contact stresses are considerably different compared to the classical Savin’s solution that ignores the influence of the radius of curvature of the liner. The latter two problems refer to the drilling and indentation processes in rocks. The equivalence of these two contact problems is demonstrated based on experimental results, as well as on analytical and numerical solutions.