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The article discusses a contour element method applied to numericalsimulations of crack propagation trajectories in elastic structures. Because theboundary integral equation degenerates for a body with two crack-surfaces occupyingthe same location one of the forms of the displacement discontinuity method isimplemented. According to the implemented method, resultant forces and dislocationdensities, which are placed at mid-nodes of contour segments on one of the cracksurfaces, are characterized by the indirect boundary integral equation. Contrarily tointernal crack problems, for edge crack problems an edge-discontinuous element isused at the intersection between a crack and an edge to avoid a common node at theintersection. New numerical formulations that are built up on analytical integration areimplemented. Therefore, all regular and singular integrals are evaluated onlyanalytically. Tractions and resultant forces at a mid-node of any contour segment areregularized by a nonlocal characterization function. Hence, values of their componentsare obtained from the modified form of Somigliana’s identity that embraces nonlocalelements and standard elements of kernel matrices used in the boundary elementanalysis.