The relationship between the strain energy release rate, G, and the displacements of the surfaces of an extending crack in an elastic, tensile member is examined. It is shown that G can be expressed in terms of the volume of the deformed crack provided that any stresses applied to crack surfaces are uniform. This form is especially useful for superposition applications as it depends linearly on displacements. The strain energy release rate is calculated from crack volumes for a crack in an infinite sheet and for two cases of a crack in an infinite solid: (a) a penny-shaped crack subjected to internal pressure as well as axial stress, and (b) an elliptical crack loaded by axial stress. The importance of the shape of the propagating crack is demonstrated by the elliptical crack by considering various shapes for the propagating crack such as preferential propagation along a diameter or propagation as an ellipse of invariant shape. A discussion of the distinction between a fracture criterion based on the strain energy release rate and one based on the stress intensity factor is presented.