We study deadlocks using geometric methods based on generalized process graphs [Dij68], i.e., cubical complexes or Higher-Dimensional Automata (HDA) [Pra91,vG91,GJ92,Gun94], describing the semantics of the concurrent system of interest. A new algorithm is described and fully assessed, both theoretically and practically and compared with more well-known traversing techniques. An implementation is available, applied to a toy language. This algorithm not only computes the deadlocking states of a concurrent system but also the so-called “unsafe region” which consists of the states which will eventually lead to a deadlocking state. Its basis is a characterization of deadlocks using dual geometric properties of the “forbidden region”.