The study considers the problems relating to vocational training of specialists in the virtual educational environment of a higher education institution. The use of advanced information and communication systems (electronic mail, electronic teleconferences, electronic and information resources including text, visual, audio and video information) and virtual technology (Daydream, Vive VR, technology of virtual games) in the educational process of a higher education institution enables to realize an interactive communication of the participants of this process. The article presents the experience on introduction of the virtual educational environment using LMS Moodle, and the authors consider the influence of such environment on the interactive engagement of the students and teachers from the universities in Kazakhstan and Slovakia. We have tried to demonstrate how the LMS Moodle platform helps arrange e-learning, conduct lessons in electronic classrooms, take online courses, and conduct synchronous and asynchronous learning. The developed online tasks allowed for the monitoring of the students' progress in all the educational activities. The results of the experiment helped guide the choice of follow-up study in this area.