It is an obvious fact that residual stresses can have a detrimental effect on the mechanical integrity of structures. Measuring such stresses can often be a tedious task and for that reason sharp indentation testing has been proposed as an alternative for this purpose. Correlation between global indentation properties and residual stresses has been studied quite frequently, and a solid foundation has been laid down concerning this issue. Empirical, or semi-empirical, relations have been proposed yielding results of quite good accuracy. Further progress and mechanical understanding regarding this matter will require a more in-depth understanding of the field variables at this particular indentation problem and this is the subject of the present study. In doing so, finite element simulations are performed of sharp indentation of materials with and without residual stresses. Classical Mises plasticity and conical indentation are considered. The main conclusion from this study is that the development of stresses in materials with high or medium-sized compressive residual stresses differs substantially from a situation with tensile residual stresses, both as regards the level of elastic deformation in the contact region and the sensitivity of such stresses. Any attempt to include such stress states in a general correlation effort of indentation quantities is therefore highly unlikely to be successful.