Indentation testing is a convenient means to study mechanical properties of thin coatings. We suggest a new method to identify the viscoplastic behavior of a polymer by using the force-penetration curves during nano-indentation testing performed with two indenter shapes. During loading, the load applied by the indenter and the penetration depth have been measured. These force-penetration curves have been compared to the load computed by using the finite element method with a two dimensional software. The viscoplastic behavior of the polymer is modeled with the G'sell-Jonas law. The main particularity of this law is the modeling of the large strain-hardening at large strains. The unknown parameters of this law have been obtained by fitting computed and experimental force-penetration curves. We have identified each parameter independently of the others by taking into account the indenter tip defect. The nano-indentation tests have been performed with three strain rates and with two indenter shapes: a Berkovich indenter and a cone with a semi angle of theta = 30degrees and a tip radius. In this paper, the polymer is a polycarbonate. Several authors have made rheological tests on this polymer. The true strain-true stress curve obtained with our method is in good agreement with the compression curve.