Due to the complex geological conditions, the construction of underground tunnels in the rocks exhibiting creep behaviors is a great challenge and the structures’ long-term stability is of main importance. The excavation by tunnel boring machines (TBM) of a tunnel that is supported by a double flexible/concrete liner is considered a potential technical solution. However, the efficiency of such a support system on the stability at long-term of a tunnel must be verified in the real condition by considering both the effects of uncertainties of the time-dependent rock behavior and anisotropy of initial stress state. In this paper, the subset simulation and the Sobol global sensitivity analysis are chosen to estimate the failure probability of the tunnel supports and quantify the importance of different random parameters, respectively. The results reveal that considering the anisotropy of initial stresses increases the failure probability, especially in the concrete support elements. In addition, the parameters of initial stresses are the ones of main importance for both liners according to the Sobol indices. Therefore, the anisotropy of initial stresses and the related uncertainties should be considered for reliable tunnel designs.