Material characterization of soft biological tissues by mixed experimental/numerical (inverse) techniques represents a powerful tool for the analysis of their complex mechanics. However, the uncertainty related to the accuracy and capability of the technique is not yet completely investigated and understood. In this work, a quasi-static indentation procedure is implemented in order to extract the Mooney-Rivlin material parameters and the equivalent Young's modulus for a hyperelastic rubber-like material. A non-standard approach based on a Finite Element (FE) inverse method is employed. An experimental set-up consisting of a dedicated micro-indentation system has been employed to extract reaction force values as a function of the penetration depth. A cost function, based on the square difference between experimental and numerical data, is optimized trough a modified Nelder-Mead direct search algorithm (MNMA). The accuracy of the identified parameters is discussed using results of a virtual benchmark case study.