Concavity trees are structures for 2-D shape representation. In this paper, we present a new recursive method for concavity tree matching that returns the distance between two attributed concavity trees. The matching is based both on the structure of the tree as well as on the attributes stored at each node. Moreover, the method can be implemented on parallel architectures, and it supports occluded and partial matching. To the best of our knowledge, this is the first work to detail a method for concavity tree matching. We test our method on 625 silhouettes in the context of shape-based nearest-neighbour retrieval.