Spring 2020 saw most Russian universities’ switch to distant learning due to the threat of COVID-19. The forced transition imposed new demands on faculty and students, who had to quickly adapt to the new educational conditions. These changes raised concerns about the quality of distant learning. The purpose of this study was to identify which students expressed more anxiety on expecting difficulties associated with a lack of understanding educational material under new circumstances. The study was based on the data of 6,230 Ural Federal University students polled in March 2020. Regression data analysis showed that the fear of not being able to cope with learning was more typical for the 1st and the 2nd year bachelors, for students who lowly estimate their self-regulated learning skills, for students who expected difficulties of communicating with teachers and of being motivated, as well as for students who attended classes for the sake of learning. The authors discuss possible measures to support students in the conditions of rapid and mass transition to distant learning.