Using Cultural-Historical Activity Theory, we analyze lecturers' views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between the lecturers' professional identities and the structure of university degrees. Our conceptualization of these tensions might help lecturers consider how to overcome obstacles in their own contexts.