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AFM nanoindentations show a dependence of penetration, i.e., the relative motion between the sample and the tip (indenter), on material elastic properties when using the same load. This relationship becomes visible by using of samples being homogeneous down to the scale of nanoindentation. They were prepared from materials covering a broad range of mechanical behavior: from rubbery networks to glassy and semicrystalline polymers. The elastic modulus can be obtained applying Sneddon's elastic contact mechanics approach. To do this, some calibrations and instrumental features have to be measured accurately. All the polymers tested show that the contact between the tip and the sample is dominated by elastic behavior with negligible plastic deformation. In contrast to a standard metallic material like lead, the penetration dependence on load follows an exponent of 1.5, consistent with elastic contact mechanics. This can be justified on the basis of the large elastic range polymers exhibit, on the constraints due to the geometry of the deformation during indentation and to the critical yielding volume needed in order to induce plasticity. For the polymers studied, this volume is chosen in such a way that a significant material volume is irreversibly deformed. Elastic moduli taken from AFM force curves show a very good agreement with bulk values obtained by macroscopic tensile testing, on all the polymers tested. This result confirms that AFM nanoindentations in polymers take place mostly in the elastic range and opens the possibility to characterize the mechanical behavior of polymers on an unparalleled small scale compared to commercial DSI (depth sensing instruments), which use a much blunter indenter.