This article reviewed the structure of design activities, special aspects of the specialists' training in multi-disciplinary design environment, the formation process of their cultural and professional competences, necessary for artistic, creative and research activities in the field of design. It identified the components of the national indigenous culture in the formation of the design of objects, problem of continuity in the development of different areas of the material and artistic culture. It substantiated the role of intersubject communications in the formation of professional competences of students-designers and the value of discipline "History of traditional culture" in the professional and artistic training of future designers. It characterized ways of making graphic design, with account of folk art traditions. It defined methods of integrated education in vocational and artistic activities. It proposed pedagogical conditions of future designers' professional competences formation based on acquiring scientific knowledge and specific technical skills.