The discrete crack-concept is applied to study the 3D propagation of tensile-dominated failure in plain concrete. To this end the Partition of Unity Finite Element Method (PUFEM) is utilized and the strong discontinuity approach is followed. A consistent linearized implementation of the PUFEM is combined with a predictor-corrector algorithm to track the crack path, which leads to a robust numerical description of concrete cracking. The proposed concept is applied to study concrete failure during the PCT3D test and the predicted numerical results are compared to experimental data. The proposed numerical concept provides a clear interface for constitutive models and allows an investigation of their impact on concrete cracking under 3D conditions, which is of significant scientific interests to interpret results from 3D experiments.