The main problems of the development of the higher education system in the Russian Federation, characteristic of both the federal system as a whole and its regional components, are considered. The directions of solving these difficulties in order to improve and effectively develop, ensure the state order for education are proposed. This includes the development of communication systems, distance learning, issues of expanding the training of foreign students. The possibilities of modeling the processes of functioning and development of educational institutions based on the use of the methodology of scenario research of complex systems are considered. A basic simulation model of an educational institution based on the method of constructing operator graphs is proposed