The health of а person and his capacity for work under conditions of high mountains in тапу respects is deter mined bу the reliability of the function of physio logical systems. Mathematical methods of both the reliability theory and mathematical simulation of basic functional systems are proposed to bе used for investigating the reliability. It is shown that the most suitable reliability model for living systems is а chain model-a successive connection of links representing separate functional systems of organism. Besides, the weakest links determining the reliability of functioning of the whole organism under the extreme conditions of high mountains even for а healthy person are-respiration, blood circulation, thermoregulation and psychophysiological systems. Quantitative characteristics of the reliability of these systems are determined through the main indicators. The influence of non-sufficient contents of охуgen in respiration mixture, low atmospheric pressure, low temperatures of the environment are simulated by computer models of organism. An analyses of modeling data shows that moderate physical loading improves indicators of organisms adaptivety to external conditions of high mountains and promotes the increasing of persons саpacity for work and the reliability of his functioning.