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The present paper deals with the global criterion based on a variationalprinciple of the crack theory to estimate the crack path in the case of brittle fracture.The variational principle of the crack path on the surface of a solid as the minimum ofthe certain functional was formulated. The crack path is interpreted as a generalizedgeodesic line on the solid surface. Crack path estimations based on a variationalprinciple have been done for a circular cone under torsion, a plane weakened by acircular hole, a half-plane under a concentrated force.