It is well known that the energy release rate associated with translation, rotation and self-similar expansion of defects in solids are expressed by the path-independent integrals J, L, and M, respectively. It is shown that these integrals for a crack or a circular hole may be obtained by first considering an elliptical cavity and then performing a limiting process. This obviates dealing with singularities at the crack tip. The energy release rates for these defects under various mechanical, thermal and electromechanical loading conditions are calculated.