Recently, it has been observed that the crack along the interface of non-homogeneous materials propagates exceeding transonic of the compliant material. This range of crack velocity is not possible to achieve in a homogeneous material. In our previous studies, the transonic interfacial fracture phenomena in bimaterial specimens of PMMA and aluminum alloy were experimentally recorded by using an ultrahigh-speed video camera. And the histories of the stress gradient distributions near the interface were also observed by the C.G.S method. In the experiment, it was observed that two cracks along the material interface coalesced and after that a circular stress wave propagations occurred into the compliant material side. In this study, dynamic interfacial crack propagation is simulated by the moving finite element method based on the Delaunay automatic mesh generation, which accurately satisfy the boundary conditions in front of and behind the propagating crack tip. In the numerical simulation, the stress gradient waves occurred with the crack coalescence are successfully visualized in 3-D form. Furthermore, it succeeded in calculating efficiently the separated dynamic J integration value in case two or more cracks coalescence by using s-function, and it will be found that the dynamic J integral is non-zero even for transonic fracture region and the most of the energy release rate is provided from the more compliant material PMMA.