Accurate prediction of the breakout capacity and crack path of post-installed anchors remains a demanding problem, owing to the nonlinear behaviour of concrete and the sensitivity of the numerical response to the discretisation. This study investigates, within the mesh fragmentation technique, the influence of element type and orientation on breakout capacity, crack path and post-peak behaviour. A two-dimensional plane-strain model was developed in ANSYS and validated against an anchor pull-out test on concrete with a compressive strength of 30 MPa and an embedment depth of 60 mm. Concrete nonlinearity was represented by the Menetrey–Willam yield surface and crack propagation by a cohesive zone model. Four mesh arrangements — quadrilateral, antiparallel, parallel and irregular — were analysed together with a continuum model. The novelty lies in the systematic assessment of mesh orientation effects and in a fragmented-mesh generation algorithm that automatically creates potential crack surfaces between adjacent elements. The quadrilateral and antiparallel meshes overestimated the breakout capacity by approximately 37% and 15%, respectively, and produced a stepped crack path. The parallel model predicted the peak capacity within 2%, but exhibited a steeper post-peak load drop. The best agreement was obtained with the irregular model, with a capacity error below 1% and a crack angle of approximately 34°. The continuum model overestimated the capacity by about 42%. Despite the limitations of the two-dimensional idealisation, the results indicate that a random distribution of element orientations appreciably improves the accuracy of failure prediction.