A numerical study on a stretch of the Brenner Base Tunnel, characterized by high overburden and driven according to the New Austrian Tunneling Method, is presented. At first, a 3D time-dependent nonlinear finite element model is developed, taking into account the construction process, nonlinear material behavior of the surrounding rock mass, and the time-dependent nonlinear material behavior of shotcrete. Next, the prognosis capabilities of a simplified time-dependent 2D model are investigated, since in engineering practice 3D computations are often not feasible due to their computational expense. For this model, a thorough calibration of a particular stress release scheme based on the 3D model is performed, aiming at a good fit of the displacements. Hence, the remaining discrepancies of the response of the two models can be attributed to the simplifying assumptions inherent in the 2D model. The computed displacements are validated by comparison with in situ measurement data. It will be demonstrated that both the 3D model and the calibrated 2D model together with the nonlinear constitutive models allow a good correspondence of the predicted displacements with the measured ones at the tunnel site. However, striking discrepancies are observed for the predicted evolution of the stress state in the shotcrete shell.