Abstract: We develop athree-dimensional finite-deformation cohesive element and a classof irreversible cohesive laws which enable the accurate andefficient tracking of dynamically growing cracks. The cohesiveelement governs the separation of the crack flanks in accordancewith an irreversible cohesive law, eventually leading to theformation of free surfaces, and is compatible with a conventionalfinite element discretization of the bulk material. Theversatility and predictive ability of the method is demonstratedthrough the simulation of a drop-weight dynamic fracture testsimilar to those reported by Zehnder and Rosakis$^{[1]}$. Theability of the method to approximate the experimentally observedcrack-tip trajectory is particularly noteworthy.