Abstract: The scope of application of the path independence of J integral in bimaterial with a crack, which is parallel or vertical or inclined to the interface, is discussed in this paper. According to the conservative law of J integral for the bimaterials with a crack paralleling the interface, a hypothesis about independence of the values of the type Ⅰ fracture strain energy release rate(SERR) from the location of the crack paralleling and closely near the interface is forwarded. And it is verified with finite element method(FFM). A schematic model for a skew crack being near the bimaterial interface is provided. The variation law of SERR with the Dundur's parameters and the angle θ between the interface and the crack surface is calculated by FEM. A method for calculating the stress intensity factor through the SERR for a skew crack near the interface is also given in the paper.