While new cohorts of students, with an increasing awareness of the importance of foreign languages, especially English, are arriving at the universities, English-medium instruction (EMI) is one of the main instruments to internationalise universities. However, research on attitudes of teachers and students towards EMI programmes is scarce in higher education, especially in the area of Engineering. In this article, we study the instructors' and students' attitudes, motivation, and expectations towards the implementation of English-taught programmes at an Engineering Higher Education institution. The participants in this study were teachers and students at the School of Agricultural Engineering of the Technical University of Madrid (UPM), Spain. Our results shed some light on different aspects of students' and instructors' considerations towards EMI at tertiary education. They might also help to promote institutional policies as well as to face up challenges of the implementation of EMI university programmes in Engineering.