A concurrent multiscale method is developed for simulating quasi-static crack prop-
agation in which the failure processes occur in only a small portion of the structure. For this pur-
pose, a multiscale model is adopted and both scales are discretized with finite-element meshes.
The extended finite element method is employed to take into account the propagation of discon-
tinuities on the fine-scale subregions. At the same time, for the other subregions, the coarse-scale
mesh is employed and is resolved by using the extended multiscale finite element method. Several
representative numerical examples are given to verify the validity of the method.