This work introduces a phenomenographic analysis of the concept of flexibility in the domain of production science. Flexibility is a cornerstone in the education of industrial and production engineers; however, it still appears as a broadly and even inconsistently defined construct. In order to clarify what is or should be learnt, this work analyses first the established literature to extract a working characterisation of the flexibility concept. The resulting understanding is then used to represent the experts' perception of the topic, which in turn is used as the ideal level of understanding that a student should achieve herself/himself when studying such a concept. The second phase of the work aims at disclosing and classifying the multifaceted perceptions of flexibility that two classes of industrial engineering students have after two courses in which the focal concept of manufacturing flexibility has been presented using two different approaches. The research is based on a survey completed by students. The data collected have consequently been structured into a finite set of clusters according to: a) the level of understanding of the key concept; and b) the nature of the shown knowledge. The classification is, then, the basis for defining an epistemologically sound approach to develop suitable teaching and learning activities to ensure optimal acquisition of the concept of flexibility.