Instrumented nano-indentation has been widely used throughout the last decades as an efficient non-destructive test for local mechanical characterisation of several types of materials. However, The appli-cation of nano-indentation on elastomeric materials remains limited and quite a difficult task given theircomplex mechanical and structural characteristics [1].In the present work, we try to overcome these experimental limitations and find an effective numericalapproach for local mechanical characterization of hyper-elastic materials. For such needs, a numeri-cal study based on shape-manifold learning method [2] was carried out using nano-indentation load-displacement curves.In this approach, we construct a reduced order model (shape manifold) from a set of high-dimensionaldata (nano-indentation curves) generated from numerical nano-indentation tests, through a design ofexperiments (DoE) and using proper orthogonal decomposition (POD) combined with the kriging inter-polation method. Then, the inverse problem is solved using an optimization algorithm minimizing thedistance between the shape manifold and the projected experimental data (curve) in the reduced shape-space to finally identify its desired parameters.Besides, and based on the same process, we study the influence of the indenter geometry, the frictioncoefficient variation and the indented material height effect.Regarding the complexity of usual hyper-elastic behaviour laws, our ongoing study has shown that theshape-manifold learning approach is a promising solution in order to estimate the intrinsic dimensional-ity, relieve the computational cost, adapt the loading conditions and finally identify material parametersof a given elastomer from nano-indentation curves.