The bodies are considered as consisting of smooth surfaces and homogeneous materials. A continuum approach is taken where the stresses, strains and displacements are described by (piecewise) continuous functions. The half-space approach is an elegant solution strategy for so-called "smooth-edged" or "concentrated" contact problems. Using the fundamental solution for the half-space, the full 3D contact problem is reduced to a 2D problem for the bodies' bounding surfaces. A further simplification occurs if the two bodies are “geometrically and elastically alike”. In general, stress inside a body in one direction induces displacements in perpendicular directions too. Consequently, there is an interaction between the normal stress and tangential displacements in the contact problem, and an interaction between the tangential stress and normal displacements. But if the normal stress in the contact interface induces the same tangential displacements in both contacting bodies, then there is no relative tangential displacement of the two surfaces. In that case, the normal and tangential contact problems are decoupled. If this is the case then the two bodies are called "quasi-identical". This happens for instance if the bodies are mirror-symmetric with respect to the contact plane and have the same elastic constants. Classical solutions based on the half-space approach are: