In this article, a new method for determination of elastoplastic properties from an indentation loading curve is proposed. Mathematical model, based on deformation theory, leads to quasi- static elastoplastic contact problem, given by the monotonically increasing values alpha(i) > 0 of the indentation depth. The identification problem is formulated as an inverse problem of determining the stress-strain curve sigma(i) = sigma(i)(e(i)) from an experimentally given indentation curve P = P(alpha). The inversion method is based on the parameterization of the stress-strain curve, according to the discrete values of the indentation depth, and uses only a priori information as monotonicity of the unknown function sigma(i) = sigma(i)(e(i)). It is shown that the ill- conditionedness of the identification problems depends on the state discretization parameter Delta e(i). An algorithm of optimal selection of state discretization parameters is proposed as a new regularization scheme. Numerical examples with noise free and noisy data illustrate applicability and high accuracy of the proposed method.