This chapter describes the progress obtained by the authors on the development of a numerical method for the identification of material parameters from indentation experiments. An indentation experiment is performed by pressing a punch on a material sample and measuring the applied force and the indentation depth. The proposed technique minimizes a least squares cost functional using gradient descent methods. In addition, the adjoint state method is extended to variational inequalities and this permits to compute the gradient of the cost functional with low numerical cost. Using this technique, a series of identifications from indentation experiments have been done and their results are discussed in this chapter. Inverse problem is of practical interest as the indentation test does not demand the creation of complicated specimens and is simple to perform. However, the applications are restricted by the difficult mechanical interpretation of the test.