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Abstract: The article discusses the use of the percolation theory for mathematical modeling of professional education of a student. The process of getting professional education is the process of gradual formation of a number of competences. The analysis of the research works devoted to the description of the gnostic opportunities of the percolation theory in the sphere of social and social-economic processes and phenomena is undertaken. It is shown that the percolation theory can be applied to explain the transition from the quantitative changes into the qualitative ones in mathematical modeling in didactics. It is possible to use percolation theory to plan and analyze such processes as: the choice of the individual educational trajectories by the student; planning of the process of acquisition of cultural, general professional and professional competences and self-control of this process; evaluation of the level of formation of the competences that reflects the content of the result; evaluation of the level of formation of competences on the basis of the degree of comprehension of the educational program (his may help to evaluate the quality of the program as well).