Indentation test has been widely used to determine the mechanical properties of materials. In the present work, based on our previous developed inverse computation approach, we investigated the identifiability of the plastic properties of metal materials using solely the residual imprint in instrumented indentation. The indentation experiment was implemented on the Al 2024-t3 alloy, and result shows the experiment error exists unavoidably. To quantitatively investigate the influence of experiment error on the inverse derived material properties, the indentation simulation models were built, of which three different indenter shapes (conical, flat and spherical) and two different simulation set-ups (load or displacement control types) are considered. The sensitivity of the inverse problem in the relevant questions are systematically investigated. Results show the inverse problem formulated by the force control using a non-self-similar indenter is able to give more robust solution of the inverse derived material parameters. Besides, the numerical protocol was verified by application on the Al 2024-t3 alloy, and the plastic properties (yield stress and strain hardening exponent) obtained from indentation and uniaxial tests show good agreement.