The article deals with the role of Russian education in training of national personnel for foreign countries, the most important pedagogical issues of studying the process of inculturation of students in Russian universities regarding the interpretation of the concept of “inculturation” in the context of higher education, its understanding, setting boundaries and correlation with the identical concepts “socialization”, “enculturate”, “acculturation”, “assimilation”; with the development of the project characteristics of the formation of vocational inculturation for international students; the mechanisms and ways of managing this process.