SUMMARY
A complex of mathematical, algorithmic and software tools for optimization of the choice of interval hypoxic modes training is presented in this article for flying personnel. The work is aimed at increasing of adaptation, efficiency and resistance of flight crew members. The basis of the mathematical model is the mass transfer and mass exchange of oxygen, carbon dioxide and nitrogen in human organism. There is suggested the solution of problem of tissue blood circulation predictions as result of conflict situation that occurs in human organism during internal and external disturbances between executive organ tissues and self-regulation tissues. The distribution of systemic blood circulation by tissues is realized in accordance with the hypoxic or hypercapnic stimulus, therefore the problem is formulated as a quadratic programming problem. An iterative procedure for studying and estimation of the gas state of respiratory system is suggested using an interval hypoxic training, which can contribute to the professionalskill improvement of flight crews, their physical and psychological efficiency and readiness to perform complex educational and combat tasks in limited space and conditions of unfavorable external environ-ment.