Air drilling is limited to competent formations that are essentially dry. In these circumstances large shale fragments are often observed and it is believed that these large shale fragments are not from the cutting action of drill bit at the bottom of the hole but from caving in, or sloughing of the wellbore wall. This type of wellbore instability problems may occur when drilling formations have significant amounts of water-sensitive clays. Change in shale water content due to water dehydration induces additional rock stresses near the wellbore, which can destabilize the borehole. The primary cause of this problem may well relate to moisture movement. Because as air is often used as the drilling fluid, the water in exposed pores will start to evaporate into the borehole, so that the water content is reduced. This results in the development of different stress patterns and the shale fractures and falls into the wellbore. The work of this thesis simulates the shrinkage and the consequent cracking pattern. A model of a bonded granular material is created and its properties confirm it to be that of a brittle, isotropic elastic solid. Crack growth is simulated by sequentially removing the most highly stressed bond in turn. A number of different geometries are simulated and the influence of stochastic bond strength on the cracking pattern is investigated. The model results show that cracking pattern produced in the simulations is consistent with the ‘blocky’ debris sometimes seen during air drilling and so the recommendation is made that air used for drilling should be sufficiently humid to avoid the dehydration of the shale.