The use of the path independent J' integral for dynamic crack propagation, which has the physical meaning of energy release rate is numerically studied by the finite element method. Other path independent integrals are also investigated along with the J' integral. Numerical results show that the combined use of the J' integral and the finite element method is a useful tool to obtain the fracture parameters such as the stress intensity factors and the energy release rates. The use of the several other types of path-independent integrals, despite their lack of a direct interpretation as energy release rates, is also demonstrated. This is so, because the alternate path-independent integrals have been explicitly expressed in terms of the time-dependent K-factors, or the energy release rate, in the present work.