The purpose of the scientific article is aimed at studying the features of students' competence formation at tertiary educational institutions by practical training aids. To reveal the purpose of a scientific article, methods of theoretical analysis and synthesis have been used (to study the theoretical framework of students' competence formation at tertiary educational institutions by practical training aids) and methods of comparison, grouping and concretization (to analyze and assess the practical results of students' competence formation at tertiary educational institutions by practical training aids). The practical results of the study are presented through: the results of assessing students' knowledge of Mathematics, Reading and Science, according to the PISA program; dynamics and structure of the number of students enrolled in tertiary education; the proportion of undergraduate students in% of the population at the age of 20-24 years old. According to the results of the PISA program, developed by the Organization for Economic Cooperation and Development (OECD), it has been found that Austria, Belgium and Germany have the highest average scores in Mathematics, Reading and Science, compared to the average scores in OECD countries. It has been established that in Ukraine the average students' score in Mathematics in 2018 is lower than the average score in OECD countries by 21 points, in Reading -- by 36 points, and in Science -- by 20 points. In the course of the study it has been established that currently educators use the following practical training aids for the formation of students' competence in the learning process, namely: introduction of a modular academic program in the educational process, providing the necessary level of theoretical basis, implementation of introductory, educational, training, undergraduate practices, work experience internship in the educational process of students' training, application of information, innovation and interactive technologies in the educational process, teaching and training of students in accordance with the requirements of the labor market and employers, ensuring cooperation between tertiary educational institutions in the framework of student exchange programs.