The correlatioin between residual stresses and the global properties from an indentation test, i.e. hardness and size of the contact area, has been studied frequently in recent years. The investigations presented have been based on experimental, theoretical and numerical methods and as a result, the basic features of the problem are fairly well understood in the case of residual equi-biaxial surface stresses. The more general case, when the principal surface stresses are not necessarily equi-biaxial, has received nuch less attention and it is therefore the aim of the present study to remedy this shortcoming. In doing so, qualitative results are of immediate interest in this initial study but possible ways of quantitative descriptions are also discussed for future purposes. The present analysis is based on numerical methods and in particular the finite element method (FEM) is relied upon. Classical Mises elastoplastic material behavior is assumed throughout the investigation.