The article is devoted to one of the competence components of a mobile-oriented environment for professional and practical training of future software engineers. It is shown that the introduction of higher education standard 121 “Software Engineering” for the first (bachelor) level of higher education in Ukraine has generated a number of training quality assurance problems associated primarily with the low level of detailed competencies and program learning outcomes. By solving these problems, the detailed design of the system of professional competencies for future software engineers is developed. The article deals with the approaches to developing one of the most important special professional competences of future software engineers – the ability to participate in software design, including modeling (formal description) of its structure, behavior, and processes of functioning. Based on a historical and genetic review of the software engineering training practice of future software engineers in the USA, UK, Canada, Australia, New Zealand and Singapore, recommendations for choosing forms of training organization, selection of training content, ways of students’ and teachers’ activities in software engineering, modeling and designing tools; assessment of the appropriate competence formation level are formulated. The example of organizing design training in conditions close to industrial-studio training is considered. The problems of transition from architectural to detailed design and project implementation are shown. Prospects for further development of this study are to substantiate the third (after requirements engineering and design engineering) engineering component of software engineering – the software construction.