Educational institutions training engineers and technical experts operate in a dynamic environment to which they are bound to respond by developing new organizational forms for the adaptation to new conditions. The rapid development of information technology, economic situation, and hardly-predictable events like the waves of the COVID-19 pandemic and the restrictions of people's mobility pose new problems for the directors of educational institutions. The pursuit for a flexible management structure that would satisfy the current requirements brings about the necessity for a formal description of universities and their environments based on the systemic approach. The purpose of this research was to test a model based on a fuzzy cognitive map and assess the possibility of change scenario development in the education system. The authors demonstrate that this approach can conveniently describe the elements of the education system and its environment, as well as the communications and links between them. The authors obtained and analyzed the modeling results showing the possibility of using event scenarios for the facilitation of strategic decisions concerning the management of engineering education at a technical university.