Research goals: to create a web-oriented expert system on methods of optimization based on the principles of cloud technologies. Research objectives are designing and develop an expert system on based productive model of knowledge about the subject area. The object of research is a web-oriented expert system and the subjects of research are objectives and methods of optimization. In the research used the methods of mathematical modeling and computer experiment. The result of research is the knowledge base based on productive model of knowledge about the objectives and methods of optimization and developed on the it basis of web-oriented expert system for solving optimization problems. The expert system is created to guide the learning process in the preparation of mathematicians and applied mathematicians, professionals of IT and Economic Cybernetics. The main conclusions and recommendations. Web-oriented expert system created for use in the educational process at university training in mathematics, applied mathematics, information technology and economic cybernetics. In the future development of software modules for solving some classes of optimization problems directly on the site of an expert system that will enable use it to solve real problems of small and medium businesses.