Abstract: An expression of energy difference rate in a plate of non-uniform thickness with a crack of mixed mode under both body force and surface tractions in a non-uniform temperature field is derived.From it a two-dimensional generalized J integral of mixed mode can be defined as following:On the basis of the above definition it is proved that the two-dimensional generalized J integral of mixed mode is independent of integration path.According to the path-independence and the singularity of the stress field in the vicinity of a crack tip,the relation between the two-dimensional generalized J integral of mixed mode and the stress intensity factors in a linear elastic case is deduced as following:When the two-dimensional generalized J integral of mixed mode is calculated by conventional finite element method,the stress intensity factors k1 and k2 in a linear elastic case can be obtained from the above formulas.This paper also demonstrates that the crack tip is not the singular point of temperature field.