Questions of development of expert system for the decision of problems of training are considered. The structure of expert system is resulted. Authors develop model of success of training. With use of the given model forecasts of success of training on mathematics for separate pupils have been made. Authors work a theoretical part of expert system. The theoretical and practical part of a database for students of mathematical, economic, sociological and legal faculties of high school is developed. The results received with the help of expert system, are compared to a real final level of knowledge of the chosen students. The given expert system will allow to optimize process of training, to select an individual approach for each student, to make the forecast of success of training.