The traditional ‘no property’ approach of the law to human biomaterials has long been punctured by exceptions. Developments in the jurisprudence of property in human tissue in English law and beyond demonstrate that a variety of tissues are capable of being subject to proprietary considerations. Further, among commentators, there are few who would deny, given biotechnological advances, that such materials can be considered thus. Yet, where commentators do admit human biomaterials into the realm of property, it is often done with an emphasis on some sort of separation from the person who is the source of those materials. One line of argument suggests that there is a difference between persons and things, which constitutes a morally justifiable distinction when it comes to property. This article examines whether the idea of separability can do the work of demarcating those objects that ought to be considered property from those that ought not to be. It argues that, despite the entailment of a separability criterion inherent in both the statutory and common law positions, and the support given to this by some commentators, it is philosophically problematic as the basis for delineating property in human tissue and other biomaterials.