International cooperation in all professional settings makes translation a very important tool of interpersonal and professional relations of specialists in different domains. Training of undergraduates and graduates' translation skills in a special setting is included in the curriculum of non-linguistic higher education institutions and studied from various aspects. The objective of the paper is to consider some psychological and teaching issues related to translation as a language activity. Russian and foreign researchers' works and the findings of the practical experience of Foreign Languages Department of Law Institute, Peoples' Friendship University of Russia are presented. The survey of the specialists with different practical experience of translation in the law setting is analyzed. The examination of training translation in the law setting at non linguistic higher education institution is provided. The data of the current research can be used in teaching practice to develop the translation skills of the undergraduates, graduates and postgraduates.