Abstract In two previous articles by Carlsson and Larsson [S. Carlsson, P.-L. Larsson, On the determination of residual stress and strain fields by sharp indentation testing. Part I. Theoretical and numerical analysis, Acta Mater., 49 (2001) 2179–2191; S. Carlsson, P.-L. Larsson, On the determination of residual stress and strain fields by sharp indentation testing. Part II. Experimental investigation, Acta Mater, 49 (2001) 2193–2203], sharp indentation tests were analysed experimentally, theoretically and numerically and it was found that biaxial residual stress and strain fields could be correlated with the global properties, i.e. hardness and size of the contact area, given by such tests. The practical usefulness of this finding is limited though due to the fact that the global properties are only weakly dependent of the residual stress state when standard indenter geometries are at issue. In order to find some guidance for improving upon this situation a numerical study of sharp indentation testing, based on the finite element method, was performed. The results derived indicate that the sensitivity of indentation variables to stress can be significantly increased by increasing the inclined angle of the sharp indenter and that this feature can be accurately captured by previously derived closed form relations directly applicable to a practical situation.