This study presents a numerical analysis of the initiation and propagation of cracks in a rock mass, accounting for installation clearances in the undercut anchor–borehole system. This is important for the context of rock de-consolidation technology and the assessment of the load-bearing capacity and performance of undercut anchors, where actual installation conditions deviate from ideal assumptions. In particular, the limitations of classical failure cone models are highlighted, as they do not reflect the actual trajectory of fracture propagation in brittle media. The aim of this study was to determine the influence of geometric clearances (l₁, l₂) between the anchor and the rock mass on the location of the fracture initiation point and the course of its propagation. The analysis was performed using the finite element method with the XFEM implemented in ABAQUS. Five clearance combinations in the range of 0–1 mm were considered, with a constant effective anchorage depth (hef = 70 mm) and unchanging material and geometric parameters of the system. The results indicate that, within the analyzed range of clearance values, their effect on the crack-propagation trajectory is negligible, and the crack paths are similar. However, it was found that, in selected configurations, the location of the crack initiation point may change, due to local stress redistribution in the contact zone, particularly near the drive screw tip. These results confirm that factors such as the rock's mechanical properties, the anchor head's geometry, and contact conditions are more significant in forming the failure zone than minor potential installation clearances. The conducted research makes a significant contribution to the development of methods for analyzing the performance of rock bolts in rock masses, indicating the limited significance of geometric imperfections within the analyzed scope and emphasizing the need for further research that accounts for more complex operating conditions of the system.