Abstract: In order to investigate the stability of the case/insulation,insulation/cladding,cladding/propellant interfacial cracks in the solid rocket motor (SRM) grain when it was lunched,the three-dimension viscoelastic finite element models of the SRM with interfacial cracks were established.The singular interfacial crack elements were included in the 3-D <i<J</i<-integral loop surface to improve the calculation precision.The three-dimension singular interfacial crack elements at the tips of debonded cracks were established to simulate the crack propagation along the bonded interface.Along the interfacial crack propagation,the <i<J</i<-integral of the interfacial crack tips variation with the debonded length and position were calculated to prejudge its stability.The results show that the maximal <i<J</i<-integral value of the interfacial cracks is located in the position where corresponds to the fore slot of SRM grain.And the <i<J</i<-integral value of the interfacial cracks is monotony increasing with the debonded length.Then the interfacial cracks should be expanded instability at a certain debonded depth.