Dynamic fragmentation is a rapid and catastrophic failure of a material. During this process, the nucleation, propagation, branching, and coalescence of cracks results in the formation of fragments. The numerical modeling of this phenomenon is challenging because it requires high-performance computational capabilities. For this purpose, the finite-element method with dynamic insertion of cohesive elements was chosen. This paper describes the parallel implementation of its fundamental algorithms in the C++ open-source library Akantu. Moreover, a numerical instability that can cause the loss of energy conservation and possible solutions to it are illustrated. Finally, the method is applied to the dynamic fragmentation of a hollow sphere subjected to uniform radial expansion. Copyright (c) 2016 John Wiley & Sons, Ltd.