Respiratory system diseases are among the most dangerous for human life. Pathologies of the respiratory system appear due to environmental pollution, the spread of epidemics, etc.. To predict the course of pathological processes, the body's response to various influences of external extreme conditions, there is a strong need to develop the imitational mathematical models, which can provide the opportunity for the fast selection of the necessary optimal breathing mode. The goal of the work was to develop the imitational mathematical model to prognose and regulate the state of the respiratory system of the organism under the indignation of the environment. To study the mechanisms of self-regulation and adaptation of the body to disturbances of the external or internal environment, a mathematical model of the functional respiratory and circulatory system was developed. The dynamics of the partial pressures and stresses of the respiratory gases in the structures of the body was described by a system of ordinary differential equations. The principles of material balance and continuity of the flow were used to construct them. The structure of the model considered several reservoirs of the alveolar space, each of which was connected to the environment by a separate section of the airways and was washed by the corresponding volume of blood in the pulmonary capillaries. On the basis of the mathematical model of the functional respiratory system, an imitational mathematical model of the gas exchange process in the lungs has been developed and investigated. The model took into account the role of the elasticity and the resistance of the lung structures in the formation of the nature of the gas exchange process under various modes of external respiration. The results of the research will allow to accelerate the selection of the optimal breathing mode to achieve a stable balance of the internal and the external environment of the body.