The nanoindentation test is a fundamental tool to assess the link between morphology and mechanical properties. The preliminary results of a more exhaustive study about the applicability to polymers of the most used procedure to determine elastic modulus by indentation are reported in this short communication. A departure of the experimental conditions from the theoretical assumptions and results that give rise to the Oliver and Pharr analysis is shown to occur under a wide range of experimental conditions, with applied loads and penetration depths covering several orders of magnitude and using different indenter geometries. Unloading curves with exponents significantly larger than 2 are observed in disagreement with the contact mechanics approach used by Oliver and Pharr.