The artificial neural networks (ANN) for the psycho-diagnostics data analyzing is used. It is shown that the training of a simple ANN of direct propagation, as the problem of nonlinear multi-parameter optimization, allows to carry out the vertical system analysis and to assess the latent, non-linear relationship between different level’s psychological characteristics (the system of relationships, motivational characteristics, personality traits, intelligence, the type of nervous system). The detection of such links using the traditional for psychology the correlative ore factor analysis is difficult. Quantitative criteria are proposed for evaluating the quality of ANN algorithms, which are based on a scattering diagram and the statistical distribution of errors in the learning and testing of a neural network. As an example, the data of psycho-diagnostics of younger adolescents are analyzed. The proposed algorithms and criteria made it possible to detect latent links between psychological characteristics, to evaluate the ratio of psychological level-based indicators.