A theory of fracture of materials is developed which encompasses shear and tension failure. The probability of fracture occurring across a given surface element in an isotropic medium is assumed to be a general function of the limiting normal and tangential stresses across that element. A modification is later introduced to allow for anisotropy wherein the medium has a single plane of weakness.The probable fracture at a point in an isotropic medium is predicted to take place across a pair of conjugate surface elements, equally inclined to the direction of the maximum pressure at an angle which is a function of the limiting stresses as well as constants of the medium. In anisotropic media failure is predicted generally across a single surface element. Applied to geology the theory accounts for certain types of faults, jointing in rocks, for certain effects of increase in depth, and for the deflection or termination of a fault by an earlier fault or shear zone.