Abstract: Proposing a counter example,it is proved that J integral is not conservative in regional heterogeneous media.Noticing the discontinuity of stress and strain components somewhere,J^* integral is presented to modify J^* integral.The pathindependence and the physical meaning of the J^* integral,and the energy expression J^*=-1∂U/B∂a are verified simply.The concept and the constitution approach of interface elements are put forward for regional heterogeneous media in elastoplastic FEM analysis.