A special crack tip element is developed to model the feature of a stress singularity at a crack tip, based on an elastic solution for an arbitrary displacement discontinuity. By incorporating this crack tip element into the conventional displacement discontinity method, the propagation of a crack with an arbitrary configuration can be modelled using the Griffith-Irwin energy criterion in a linear elastic medium. The accuracy and consistency of the method is illustrated by various examples; the results are seen to be in excellent agreement with the exact analytical solutions and the known experimental evidence. The study shows that the displacement discontinuity method is efficient and has a potential for modelling the behaviour of a complex crack. © 1990.