Teaching engineering students critical appraisal skills that are relevant to their discipline is a key skill for postgraduate study. International English as a second language students, however, may have had limited exposure to critical thinking in their prior learning and may arrive in Australia with approaches that are problematic. Discipline-specific English for Academic Purposes (EAP) courses integrated in the Engineering Curriculum are an ideal, albeit challenging, environment to teach critical thinking and appraisal. This paper describes the development and student evaluation of an Engineering EAP program focussing on teaching critical appraisal to students at Melbourne University. In this paper, I describe teaching and assessment processes and qualitative feedback from an open-ended survey of three semester cohorts of students about the cross-cultural challenges of engaging with critical appraisal. The paper argues that discipline-specific EAP courses are an appropriate place to teach critical appraisal skills and that qualitative student feedback provides a useful complement to program evaluation.