The Griffith-model of brittle fracture of elastic solids and the model by Irwin and Orowan for the brittle fracture of elastic-plastic solids predict the propagation of cracks on the basis of energy supplied by the work of externally impressed forces and by the change of strain energy. Previous discussions have neglected the three-dimensional viewpoint and the body forces. Since the Irwin method of fracture-strength analysis has become of increased interest, especially with respect to rotor fracture, a general analysis of energy supply is presented. The analysis uses Clapeyron’s theorem and Betti’s reciprocal theorem. One of the results is that the energy supplied for crack extension equals the strain energy of the difference of the two stress fields before and after crack extension.