We present a method to model the dissolution of free surfaces of stressed crystals in contact with a fluid. The simulations are in accordance with linear stability analysis, other numerical approaches to the problem and show similarities to experiments. Free surface dissolution of a stressed crystal can lead to instabilities (ATG-instability), which strongly localize dissolution. The localization is transient and evolves from initial cusp instabilities to grooves or anti-cracks. Anti-cracks propagating into crystals may lead to brittle failure. Propagating anti-cracks show a secondary instability, a period doubling that leads to a coarsening of the structures. Anti-crack associated mode I fractures grow sub-critically and develop the same period doubling instability as anti-cracks. The simulations suggest that there is a strong physical similarity between cracks and anti-cracks. This is a further indication that anti-cracks may be associated with earthquakes as are cracks.