Abstract The present analysis concerns a finite-element study of sharp (cone) indentation of classical elastic–plastic materials with linear strain hardening and, especially, the details of the behavior of the size of the plastic zone are at issue. It is shown that the plastic zone size parameters are dependent on two parameters: the well-known Johnson parameter and the level of plastic hardening. This dependence includes both geometrical and material properties. The details of the influence from the hardening level have not been explicitly studied previously. The results are compared with previous findings for elastic–ideally plastic materials.