A rational approach to predicting the extent and shape of the fracture surface generated by hydraulic fracturing of a well is to make use of linear elastic fracture mechanics. In such an approach the different rock layers may be idealized as homogeneous, isotropic and linear elastic. A crack in a given rock is assumed to advance when the stress intensity factor at the crack tip is equal to the value for which crack growth is observed in laboratory fracture experiments. Even with these idealizations the problem remains extremely difficult because (a) the problem is inherently 3-dimensional, (b) the problem is one of undetermined boundaries in that the location of the crack front is the subject of primary interest, and (c) the problem is complicated by the presence of layers with different elastic module. In order to make progress it is clear that further idealizations are necessary.