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New approach to strength analysis of thin-walled structural elements of anisotropicmaterials weakened by cracks under conditions of plane stress and bending isstated. The fracture criterion is grounded on the notion of the material damage measure inthe process zone at the crack tip and on the assumption of the crack growth towards thehighest possible value of this measure and its reaching the critical value. The criterion isemployed in the investigation of the critical state of the highly anisotropic plate with acrack. With the change of the loading angle in the plates with high anisotropy the instabilityof initial crack motion angle is possible. The analysis of the examples demonstrates thequantitative and qualitative impact of the proposed generalizations on the initial crackingangle and the strength of the structure.