The preferential orientation for the initiation or extension of a crack is the one which gives the maximum strain energy reduction for a given crack length. This criterion is based on the concept of maximum energy release rate, and makes no assumptions on the configuration, the homogeneity, the stress condition on the crack faces, or the material response. Consequently it is valid under the usual engineering conditions as well as under compression and high confining pressures such as obtain inside the Earth; in the latter case it replaces the empirical and approximate Coulomb-Mohr criterion. The mathematical formulation of the criterion is approached by way of constrained optimization, and the solution is proven to exist uniquely. The numerical implementation is based on a finite element scheme. An iterative method is employed to handle the material and geometric non-linearity. Test cases agree with laboratory and field data.