The article is devoted to questions of formation of cross-cultural communication on the classes with foreign students studying Russian language.. The authors propose to include reading of literary texts and their translation in the system of foreigners’ training with the aim of developing students’ practical skills of cross-cultural communication. Authors pay attention to the fact that the literary text helps to understand another culture and to overcome cultural distance. To facilitate the cultural perception of the text, the authors propose a system of reading of the adapted English literary fairy tale by Lewis Carroll " Alice's Adventures in Wonderland " in a literary translation of Boris Zakhoder. The proposed approach differs from the traditional one because, foreign readers have the opportunity to compare the world view of the English fairy tales author and the Russian translator, and also to correlate his translation from a classic translation. The article focuses on the fact that in connection with the identity of the tales author, the author of literary translation and for the foreign reader to different cultures and different national consciousnesses, the teacher together with the students-foreigners, must overcome cultural and language barriers for successful cross-cultural communication. The authors consider that the task of grammatical, lexical and communicative approach aim at achieving the text comprehension. Additional tasks of translation, that extend the capabilities of traditional work, also help. Tasks presented in the article help the student to understand the main thing: the ignorance of some of the cultural backgrounds of native speakers of a particular country does not mean that we should avoid translation work, because this work helps to learn a different language culture.