In this paper the author presents Suarez's conception on material substance in connection with two main aspects of his theory. The first aspect is 'reification' of the intrinsic principles of a composite, which has led some interpreters to the claim that Suarez significantly prepared the way for the accession of Cartesian anthropological dualism. The second one is Suarez's emphasis on the substantial unity of material composites. The analysis of the second aspect is conceived as a counterbalance to some uncharitable interpretations of Suarez's hylemorphism. In the second part of the paper the relevance of Suarez's arguments to the contemporary debates on the ontological constitution of individuals is presented.