Abstract: Three-dimensional static stress intensity factors were analyzed for a curved crack by using a second order perturbation method. The method was extended to obtain an approximate representation of a three-dimensional static stress intensity factors at the tip of a curved crack. The criterion of elastic bending crack propagation the three-dimensional body was summarized. The shape parameters of three-dimensional linear elastic bending crack propagation were figured out. A static energy release rate due to three-dimensional curved crack growth could be calculated by using Irwin’s formula. Considerations were made for a three-dimensional static curved crack in materials with inhomogeneous fracture toughness. As far as homogeneous matter was concerned, in the framework of the second-order perturbation analysis theory, the two criteria indicated the same three-dimensional static load bending crack propagation path. However, the energy criterion was superior to the stress criterion in materials with non-uniform fracture toughness. Three-dimensional static curved crack path destabilizing factors were compared and analyzed. Critical relations between the material degradation and the static applied stress or the outer static stress for various initial three-dimensional crack lengths have been studied.