Urgent problems of modernization of the Russian system of higher education in the context of the discourse of the third generation universities were revealed on the basis of the expert survey of employers (heads of personnel departments of large industrial enterprises of the city of Kazan and the Republic of Tatarstan) within research project "Strategy development of socio-economic development of the Republic of Tatarstan for the period till 2030". These include: insufficient level of professional skills and competencies of graduates in recent decades; decrease in motivation of young specialists in employment and work in the industrial sector; formal activities aimed at enhancing interaction between universities and companies due to the lack of financial and material resources. To improve the quality of young specialists` training, experts offered recommendations such as improving the system of practical training of students, modernization of the educational process through the use of new educational technologies and active involvement of employers into the development of educational plans and programs, improvement of the quality of teaching university staff.