Recently
Nishioka and Atluri have derived the path-independent J' integral which gives the energy release rate for an elastodynamically propagating crack. The J' integral is now well understood as the elastodynamic J integral. They have also shown the existence of many types of path-independent integrals which do not give the energy release rate. These various integrals can be related to the instantaneous stress intensity factors using the asymptotic near-tip solutions and the near-field path which surrounds an infinitesimal process zone. However these relations may depend on the shape of the infinitesimal process zone. In this paper, the invariance of the J' integral with respect to the shape of the infinitesimal process zone was numerically verified. The other integrals were found to depend on the shape of the infinitesimal process zone. An analytical proof for the invariance of the crack-axis component of J' integral as well as for the variance of the other integral is also given. The present paper also shows the finite limits of apparent non-integrable singularities in the J' integral. These features of the J' integral are very important for the theory and the numerical analyses in dynamic fracture mechanics.