SUMMARYThis paper delivers an e cient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on ÿnite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners has the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, it is possible to simulate crack advance in a very e ective numerical manner, including adaptive mesh reÿnement and mesh coarsening. Test examples are presented to illustrate the e ciency of the given approach. Numerical simulations of crack propagation are compared with experimental data.