The scientific-technical revolution gives us a chance to redefine ways of teaching that are being changed considerably according to recent demands. Introduction of mathematic and computer methods in training processes during learning gymnastic exercises is wide spread in modern science. This introduction is carried out in two reasonable ways: the first is creating models, that reflect sportsman's motion, and the second one is an increasing use of computer processing of sports exercise specifications data. The object of the article is to prove how important the application of modern methods in the sphere of exercise technique analysis is. The article touches upon quite a number of problems with sports exercise technique that can be solved only using biochemical research methods with such an important part as a computer technology. Using computer and video materials we can carry out deep biochemical investigation that gives us data about kinematical and dynamical structure of an observable move. Those data are the foundation to conclude whether the exercise technique is effective or not. Such an approach to solve the problem of biochemical substantiation of sports exercise rational structure consists of the following stages: gymnastic exercise video filming, determination of a body position, biochemical analysis, conclusions and exercise technique recommendations, teaching methods. The second stage (determination of a body position) involves certain difficulties, which resolution is offered in the article. The author gives a detailed description of cutting into frames sequence, using the VirtualDub computer program, and indicates its properties. Methods of body position pick-up are also represented in the article. The body position is localized in the Cartesian or polar coordinate system. The author used the polar system of coordinates to calculate biomechanical characteristics of movements. The given approach is also shown in the article. Reading of a sportsman's body links coordinates in investigated exercises, by means of the computer program developed by the author, allows to define them unmistakably and for a short time interval. Application of the received coordinates allows receiving all further necessary biomechanical characteristics of actions. The methodology described above was successfully tested and showed excellent results in making video processing period dozens times less. Such a methodology is suitable for all types of sports exercises.