Introduction. Academic performance and the results of entrance tests are the key criteria for the competitive selection of students into educational institutions for gifted children, while the psychophysiological abilities of children and adolescents, determining the possibility of learning under conditions of high academic loads, are usually not taken into account.
 The purpose of the study is to scientifically substantiate a predictive model for the selection of students into educational institutions for gifted children.
 Materials and methods. For students of a lyceum for gifted children with high mental development (Group 1) and a general education institution with an average level of mental development (Group 2), an assessment was made of risk factors for the management and intensity of the educational work, and daily routine; functional state according to integral indicators: the index of tension of regulatory systems with the determination of biological adaptation, mental performance, as well as cognitive and non-cognitive functions using modern hardware and software complexes.
 Results. The students of the lyceum for gifted children in conditions of high intensity of educational work (class 3.1), in comparison with the data of students 
 of a general education institution with optimal intensity of the educational process (class 1), were established to reveal the development of cognitive functions, 
 as evidenced by an increase in the level of mental performance by 1.3 times, it productivity and speed by 1.2 times, thinking by 1.6–2.6 times, as well as a decrease in anxiety by 17.2%, stress by 24.5% compared to the data of students of the 2nd group, an increase in stress resistance by 25.0% and cognitive activity by 22.2%. At the same time, the formation of cognitive and non-cognitive functions in students from the 1st group was ensured by a decrease in the level of biological adaptation, confirmed by the formation of a breakdown in biological adaptation in every fourth student from the 1st group (26.4%) (according to data of 33.9% among students 2nd group). As a result of correlation analysis, reliable dependences of integral indicators of the functional state of students on factors of the management of the educational process and daily routine were determined. Correlation dependencies of cognitive and non-cognitive functions on the level of mental performance and tension in the regulatory systems of students have been established, which, based on logistic regression analysis, made it possible to develop a predictive mathematical model for the selection of students in educational institutions for gifted children, based on determining mental performance, the index of tension in regulatory systems, the level mental development, anxiety, cognitive activity, resistance to stress, and stress.
 Limitation. The study is limited to a sample formed within one educational institution for gifted children.
 Conclusion. Thus, the use of a prognostic model when selecting students for educational institutions for gifted children will not only identify students with a high level of mental development, but also assess their psychophysiological abilities, predict possible difficulties in the process of educational activities, identify strong and weak personality traits associated with academic performance.