AbstractThe XFEM is known to approximate the displacements and stresses around a crack tip in a very efficient way. But as we will present in this paper we have to deal with a phenomenon coming along with this method that compels us to use higher order shape functions for those elements that are enriched by the crack tip functions.For the computation of the stress–intensity–factors we are using a J–integral over a circular domain Ω. The accuracy of the results depend on• the radius of Ω• the number of elements used in the XFEM computation• the number of nodes which were enriched by the crack tip functions (number of layers) and• the shape functions which were used for the standard FE termFor more information about the XFEM we refer to [1]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)