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Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters entering into constitutive models. The outputs of such procedures are expressed as evaluation of sought parameters in deterministic sense, while for engineering practice it is desirable to assess also the uncertainty which affects the final estimates resulting from various sources of errors within the identification procedure. In this paper an experimental-numerical method is presented centered on inverse analysis build upon data collected from the indentation test in the form of force-penetration relationship (so-called 'indentation curve'). Recursive simulations are made computationally economical by an 'a priori' model reduction procedure. Resulting inverse problem is solved in a stochastic context using Monte Carlo simulations and non-sequential Extended Kalman filter. Obtained results are presented comparatively as for accuracy and computational efficiency.