Element free Galerkin (EFG) methods are methods for solving partial differential equations that require only nodal data and a description of the geometry; no element connectivity data are needed. This makes the method very attractive for the modeling of the propagation of cracks, as the number of data changes required is small and easily developed. The method is based on the use of moving least-squares interpolants with a Galerkin method, and it provides highly accurate solutions for elliptic problems. The implementation of the EFG method for problems of fracture and static crack growth is described. Numerical examples show that accurate stress intensity factors can be obtained Without any enrichment of the displacement field by a near-crack-tip singularity and that crack growth can be easily modeled since it requires hardly any remeshing.