Current urgent issues in highr education research include the adaptation of fi rst-year students to study activities at the university, the search for a model to form an environment that can help students to adapt more successfully to conditions when they needs to show such qualities as independence, an ability to organize their time, communication, an ability to learn and self-study. The paper presents a “two-dimensional model of mentoring”, in which relationships are built between mentored student (mentees, i.e. fi rst-year students) and mentor-students (senior students), as well as between student-mentors and the teachermentor. The conducted studies revealed a number of didactic features of the implementation of mentoring in a non-humanitarian university, namely: reliance on subject-subject relations between all interaction participants, special competences of a teachermentor, compulsory procedures that provide refl ection of activities, etc. The proposed “two-dimensional model of mentoring” specifi es the goals of interaction, organizational and activity measures in the practice of mentoring, formulates the methodological principles of mentoring, and clarifi es the implemented didactic approaches. The paper presents the tasks of the mentoring subjects, the conditions that ensure a more eff ective implementation of mentoring, and the main provisions of the mentoring practice. The approbation of the practical aspects of the proposed model has proved its eff ectiveness: more successful involvement of fi rstyear students in the extracurricular activities of the university and better learning outcomes. The authors show the expediency of using the proposed model for the development and implementation of mentoring practice in a non-humanitarian university