Abstract: Since Rice J-integral has lost the propriety of path independence in the presence of secondary stresses,it can not be used to describe the stress-strain fields in the crack tip.Until now several modified J-integrals have been put out for this situation. In the paper,the physical significance and suitability of modified J-integrals have been evaluated by FEM.The relationship among them has also been discussed.Results have shown that the physical significance of given by Blackburn is clearest.It can be used as a fracture parameter in the presence of secondary stresses.