Abstract: We have derived a new generalized J-integral under the following conditions!1.The plates have variable thickness t;2.There are not only surface forces Si but also body forces Bi actingon the plates;3.The temperature distributions T are non-uniform in the plates. This work can be summarized into the followings:a . The generalized J-integral can be defined asb . According to the above definition, the generalized J-integral has the property of path-independence.c . By means of the above property, the generalized J-integral is equal to the energy release rate of the system.d . In consideration of the above equality, we can apply the generalized J-integral to determining the stress intensity factors when the nodal point displacements have been calculated by the conventional finite element method in linear elastic fracture mechanics.e . It is proposed that the generalized J-integral be used to establish the fracture criterion and crack propagation law in elasto-plastic fracture mechanics.f . Rice J-integral is a special case of the generalized J-integral.