Cracking and fracturing are one class of major failure mechanisms in brittle and semi-brittle materials. Crustal materials of the Earth can be largely considered as brittle rocks, and so cracking and fracturing phenomena are ubiquitous. Cracks created within the Earth's crust often provide a very useful channel for mineral-bearing fluids to flow, particularly from the deep crust into the shallow crust of the Earth. If other conditions such as fluid chemistry, mineralogy, temperature and pressure are appropriate, ore body formation and mineralization can take place as a result of such fluid flow. Because of the ever-increasing demand for mineral resources in the contemporary world, exploration for new mineral resources has become one of the highest priorities for many industrial countries. For this reason, extensive studies (Garven and Freeze 1984, Yeh and Tripathi 1989, 1991, Steefel and Lasaga 1994, Raffensperger and Garven 1995, Zhao et al. 1997a, Schafer et al. 1998a, b, Zhao et al. 1998a, Xu et al. 1999, Zhao et al. 2000b, Schaubs and Zhao 2002, Zhao et al. 2002a, 2003e, 2005a) have been conducted to understand the detailed physical and chemical processes that control ore body formation and mineralization within the upper crust of the Earth. Thus, the numerical simulation of spontaneous crack generation in brittle rocks within the upper crust of the Earth has become an important research topic in the field of computational geoscience.