Goal. The article is devoted to the problem of the undergraduate students’ training in the Don State Technical University in the conditions of problem education. The subject of the analysis is the developing the students’ critical thinking in the process of writing an argumentative essay. The authors aim to identify the effectiveness of the written speech in the form of an argumentative essay as a way to activate the students’ critical thinking, to define the criteria for evaluating the development of this skill. Results. The types of educational activity that determine the developing the students’ critical thinking in the process of writing an argumentative essay are determined; the subject of these essays is proposed; the subject is aimed at developing an individual point of view on the situation under discussion; the isomorphic character between writing the argumentative essay and the main stages of problem learning is established; the basic procedures and results of the experiment aimed at assessing the dynamics of critical thinking at the stages of preliminary and final testing are presented. The scope of the results. The results of the investigation could find a consistent application in the training of students in the technical and humanitarian Universities.