The subject of this study is the process of distance learning of a foreign language in a non-linguistic university. The object of the study is a system of webinars conducted during distance learning of a foreign language. The author examines in detail the structure of training webinars of various types, offers his classification of distance learning and a model of a system of distance learning of a foreign language for students of economics of a transport university, which includes an ordered system of webinars of various types. Particular attention is paid to such issues as: raising students' awareness of the structure of the discipline course and the requirements, insufficient attention to which causes students anxiety in the difficult process of distance learning. The theoretical significance lies in the creation of a classification of webinars and the development of a model of a webinar system in distance learning of a foreign language in vezu. The practical significance lies in the possibility of using the proposed or modified model of the webinar system in different learning environments and at different levels of education. After conducting an experimental training, the following conclusions were made. The introduction of an ordered model of the webinar system increases students' awareness, reduces anxiety, especially in the process of forming speaking and listening skills, improves the equipment of the educational process, as webinar recordings become more structured, orderly, and, consequently, more watchable. The educational process in the discipline "Foreign language" becomes more structured and understandable for students.