Various research is covering instrumented nano-indentation in the literature. However, studies on this characterization test remain limited when it comes to the local mechanical behavior of elastomeric materials. The application of nano-indentation on these materials is a difficult task given their complex mechanical and structural characteristics. We try to overcome these experimental limitations and find an effective numerical approach for local mechanical characterization of hyper-elastic materials. For such needs, we carried out a numerical study based on model reduction and shape manifold approach to investigate the parameters identification of different hyper-elastic constitutive laws by using instrumented indentation. Similarly, we studied the influence of the indenter geometry, the friction coefficient variation, and finally the indented material height effect. To this end, we constructed a reduced order model through a design of experiments by proper orthogonal decomposition combined with the kriging interpolation method.