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In this paper, the problem of online estimation of the mechanical impedance during the contact of a robotic system with an unknown environment is considered. This problem is of great interest when controlling a robot in an unstructured and unknown environment, such as in telemanipulation tasks, since it can be easily shown that the exploitation of the knowledge of the mechanical properties of the environment can greatly improve the performance of the robotic system. In particular, a single-point contact is considered, and the (nonlinear) Hunt-Crossley model is taken into account, instead of the classical (linear) Kelvin-Voigt model. Indeed, the former achieves a better physical consistency and also allows describing the behavior of soft materials. Finally, the online estimation algorithm is described and experimental results are presented and discussed.