n the present paper, the influence of punch tip sharpness on the interpretation of indentation measurements is considered. Firstly, in order to obtain analytical insight into the nature of the problem, closed form solutions are presented for the indentation of a homogeneous elastic half-space by an axisymmetric indenter of arbitrary shape, including Hertzian, conical, and conical indenter with a rounded tip. Next, a fast and efficient numerical implementation of a semi-analytical approach to the solution of problems about frictionless axisymmetric indentation of an elastic layer on a dissimilar substrate is described. The approach allows rapid determination of the load–displacement curves for an arbitrary punch shape. The aim of the study was to explore the implications of a finite indenter tip radius for the problem of property identification of thin films. The variation of the apparent substrate stiffness with indentation depth was established for several generic indenter shapes, namely for flat, conical and parabolic punches, and for a conical punch with a rounded tip. It is demonstrated that in each of these cases the depth variation can be described by a simple curve belonging to a family of two-parametric functions. On the basis of these findings we assess the efficiency of using different punch shapes for property determination. A procedure is proposed for this purpose which relies on the use of the depth variation profiles established here. Finally, the influence of imperfect punch shape on the accuracy of analysis is considered.