Simulation of fracture propagation with FEM method requires re-meshing to provide more accurate results. This raises a question about the determination of the direction and criterion for mesh modification. In the case of general-purpose CAE-packages, we deal with a stationary mesh, and the fracture path is usually represented as a chain of elements with degraded properties. The algorithm proposed in this paper is based on the ANSYS Mechanical APDL language for stepwise geometry reconstruction and mesh modification in accordance with the current configuration of a growing fracture and provides a more accurate description of its shape. The fracture propagation process is divided into stages. Each subsequent stage differs from the previous one by the fracture shape modified due to the crack length increment in the calculated direction. To check the adequacy of the model, an experiment on fracture propagation in glass specimens with an initial notching under uniaxial compression was performed. The laboratory experiments were carried out to determine the fracture toughness of rocks. The developed numerical model has been used to solve the problem of refracturing for different stress anisotropy in the oil-bearing rock formation.