Strain rate effects on Hardness and Young's modulus of two glassy polymers, poly(diethylene glycol bis allyl carbonate) (CR39) and bisphenol-A polycarbonate (PC), were studied in the nanoscale range. Before analyzing material behaviors, we focused on a particular phenomenon prevailing at the first stage of the contact between the surface of these polymers and the Berkovitch diamond tip used in the experiments, leading to an apparent increase of the tip defect (i.e., the missing tip of the diamond from having a shape equivalent to a perfect cone). The common methods based on calibration functions of the tip appear to be inaccurate to calculate correctly the contact area at the nanoscale range for these polymers. A new method based on Loubet et al.'s model to calculate the contact area by taking account of the apparent tip defect is proposed. The hardness values obtained this way were compared to the compressive yield stress using Tabor's relationship. A hardness-yield stress ratio close to 2.0, as expected on such polymers, was found. A strain-rate effect on the load-depth curve for these two polymers is interpreted as an increase of the hardness with the strain rate. The results from quasi-static and dynamic (the continuous stiffness method) measurements are compared. The strain-rate effect on Young's modulus in dynamic conditions should be taken into account in the hardness calculation.