Situated against the increasingly popular role of English and the internationalization of higher education, English as a medium of instruction (EMI) has become an observable phenomenon in Vietnamese tertiary education. However, there is still a dearth of studies looking at how EMI is viewed and understood by students from different disciplines. This study aims to investigate the attitude of university students majoring in natural sciences and social sciences towards EMI. By exploring the students' attitudes towards EMI, the study attempts to explain the challenges they encountered. Data were collected using questionnaires administered to 215 university students, including a group of 103 natural science students and another group of 112 social science students. The data highlight significant attitudinal differences between these two groups of students. Those majoring in natural sciences were recognizably satisfied with more obviously-defined learning intentions in EMI classes, whereas those majoring in social sciences were more concerned about their levels of concrete achievement in English proficiency. Based on the study findings, it is implied that lecturers should develop an informed EMI pedagogical competence and assist students in developing discipline-relevant EMI learning strategies.