The paper is devoted to the issues of teaching English to non-linguistic Universities' students in interdisciplinary context. The author's experience of teaching English to Bachelors and Masters studying at Institute of Law, Peoples' Friendship University of Russia is analyzed. The paper touches upon the subject of study of the Judiciary, Judges and related activities while teaching law-students English for special purposes (ESP). Brief review of the Judiciary in Russia, United Kingdom and United States of America is given here. Analysis of competence approach and orientation on professional aspects in English teaching is made. Examination of frequently used English terminological set expressions used by the Judges in their activities in Russia, United Kingdom and United States of America is specified here. Interdisciplinary and personal achievements of non-linguistic Universities' law students are accentuated. Teaching them make good use of adequate Law terminology in professional English-language communication is justified here. The necessity and actuality of professionally oriented English teaching in an interdisciplinary context, focused on the unique of its kind conceptual system of law, is stated in this paper. The mentioned issues are constantly in the center of attention of theorists, methodologists, and practitioners due to the greater than ever demands and requirements for graduates' proficiency.