Recent growth of international contacts, expanding globalization in all spheres of life and education, constant increasing number of students from different countries (Arab), the necessity to promote cross-cultural understanding conditions for better adaptation in Russian educational environment make the study relevant. The research aims to identify major socio-cultural, psychological, educational, and language challenges, which Arab students might encounter in Russian tertiary educational environment. The study was conducted among 12 international MA (Philology) students. It employed Hofstede's cultural dimensions’ theory as the leading theoretical framework via qualitative research with the data obtained from the interviews, classroom observations, and a survey. The research examined pivotal issues related to the differences and certain peculiarities of language learning in Iraq as compared to Russia. The gained experience and the data obtained during the three-year study have shown that Iraqi students lack critical thinking skills and analytical abilities due to the dominant deductive approach in language teaching in the home country. The research helped to classify major challenges with regard to expectations and requirements of the Arab students who study in Russian national research university (SUSU).