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Problems concerning the influence of the geometric parameters of an undercutting anchor on the range of the failure zone of rock medium during the pulling out of the anchor constitute one of the aspects that arouse the interest of authors due to attempts to use undercutting anchors in the process of rock lump separation. This method is considered an alternative to the existing methods of separation, especially in special cases of mining technologies. This article presents the results of numerical investigations into the effect of changes in the head geometry that occur as a result of wear on the conical part of the undercutting anchor and the extent of failure of the rock medium during its pulling out. This is an extension of considerations presented in previous work, where special attention was paid to the influence of potential errors in anchor installation, leading to changes in head geometry and, consequently, to changes in the extent of the failure zone of the rock medium. As a result, significant changes in the volume of the detached rock masses are observed. This study shows that the increasing surface friction of the stripping anchor head leads to a decrease in the angle of the undercutting head. As a result, the extent of the failure zone measured on the free rock surface increases, the value of the angle of the failure cone at the initial stage of the stripping decreases, and the deformation of rock in the plane perpendicular to the anchor axis increases.