AbstractThe development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study. In contrast to the widely used extended finite element technique, we apply a purely deformation‐based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity. This method has been applied successfully for two‐dimensional crack propagation problems in the past. However, when it comes to three‐dimensional failure phenomena, it faces the same difficulties as the extended finite element method. Unlike in two dimensions, the characterization for the three‐dimensional failure surface is non‐unique and the tracking of the discrete crack can be performed in several conceptually different ways. In this work, we review the four most common three‐dimensional crack tracking strategies. We perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency, efficiency, robustness, stability and computational cost. Moreover, we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages. The features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis. Copyright © 2008 John Wiley & Sons, Ltd.