<p>Nanoindentation is an important means to characterize the mechanical properties of materials at micro or nano scales. Current nanoindentation techniques are mainly based on the classical Hertzian contact theory for a homogeneous elastic half-space. However, it is no longer applicable when the micro/nano probe or indenter is close to a material interface or boundary, and necessary corrections are urgently needed. This paper presents an explicit solution in matrix formulation for a bi-material half-space. The solution can be successfully degenerated to the existing quarter-space or half-space solutions in matrix formulation. Furthermore, using the numerical method based on the boundary element method and conjugate gradient method, results for several typical indenters pressed into the quarter-space and the bi-material half-space, either with or without adhesion, are obtained and presented, revealing the importance of the edge effect or interface effect.</p>