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An algorithm which couples the level set method with the extended finite elementmethod to model crack growth is described. The level set method is used to represent the cracklocation, including the location of crack tips. The extended finite element method is used tocompute the stress and displacement fields necessary for determining the rate of crack growth.This combined method requires no remeshing as the crack progresses, making the algorithm veryefficient. The combination of these methods has a tremendous potential for a wide range ofapplications. A numerical example is presented to demonstrate the accuracy of the combinedmethods. In addition, a level set algorithm for modelling crack growth in three dimensions isdescribed.