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A two-level procedure designed for the estimation of constitutive model parameters is presented in this paper. The neural network (NN) approach at the first level is applied to achieve the first approximation of parameters. This technique is used to avoid potential pitfalls related to the conventional gradient-based optimization techniques, considered here as a corrector that improves predicted parameters. The feedforward NN (FFNN) and the modified Gauss–Newton algorithms are briefly presented. The proposed framework is verified for the elasto-plastic modified Cam Clay model that can be calibrated based on standard triaxial laboratory tests, i.e. the isotropic consolidation test and the drained compression test. Two different formulations of the input data to the NN, enhanced by a dimensional reduction of experimental data using principal component analysis, are presented. The determination of model characteristics is demonstrated, first on numerical pseudo-experiments and then on the experimental data. The efficiency of the proposed approach by means of accuracy and computational effort is also discussed.