The article proposes a methodology for assessing the competitive position of the university in the market of educational services, based on the development and application of the model of mutual influence of the factors of the university's competitiveness. An algorithm for assessing competitiveness is presented. The indicators of the activity of the higher educational institution that have the greatest impact on the competitive position of the university are highlighted according to the Pareto principle. A cognitive map of the situation that determines the mutual influence of the factors is constructed. A simulation model based on the integration of the principles of system dynamics and cognitive modeling, which allows the balancing of values of key parameters, is developed. The values of the model variables during the experiments can be changed, while determining the sensitivity of the vector of output parameters. Using a method based on specifying control points, a scale of characteristics for each factor has been developed. The results of modeling on the basis of real data are presented.