In the present work, a numerical study was carried out to investigate the parameters identification of hyper-elastic constitutive laws using instrumented indentation. The method applied is based on model reduction and shape manifold approach. To this end, a reduced order model is constructed through a Design of Experiments (DoE) by Proper Orthogonal Decomposition (POD), combined with the kriging interpolation method. In addition to the parameters identification, the influence of the friction coefficient is considered.