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The purpose of the work is substantiation of systemic approach and mathematical modeling methodology in studying of processes in physical education and sports. The researches were conducte as per factorial experiment of 22 type plan. In the research 92 gymnasts of age 7-10 years and 78 junior gymnasts of age 11-13 years participated. Models of junior gymnasts” trainings at initial and basic stages have been worked out. For study system’s transition to other level discriminant analysis was used. Assessment of 6-10 years boys’ motor fitness was carried out by results of motor tests. The participants were: 6 years age boys (n= 48), 7 years’-(n= 45), 8 years’-(n= 60), 9 years’-(n= 47) and 10 years’ age boys (n= 40). mathematical modeling, alongside with physical and live experiment, is one of main means for obtaining new knowledge in different spheres of natural sciences. Its importance will grow further but not replace physical and live experiment, because experience always is the base of any research. In physical education the objects of mathematical modeling include: age dynamic of cardio-vascular system’s functional state and children’s and adolescents’ motor fitness; modes of physical exercises’ fulfillment and their influence on efficiency of motor functioning; motor training of adolescents and children. For receiving models the following can be used: full factorial experiment of 2k type (models of training impacts), logistic function (determination of training process and motor abilities’ growth periods) and discriminant function (pdagogic control over fitness level). at present stage of science development …