Abstract The principal purpose of this work consists in optimizing the support system of a deep tunnel accounting for the uncertainty of the time-dependent behaviour of the surrounding rock, which is described by the rheological Burger law. The stochastic approach is chosen for this aim. On one hand the Quantile Monte Carlo (QMC) simulation is used to determine the optimal design variables (i.e., the thickness of two liners). On the other hand, the well-known Kriging metamodeling technique is undertaken to approximate the limit state function in the augmented reliability space (i.e., the tensor product between the random variable space and the design variable space). The adopted optimization process allows to derive the optimal tunnel support that verifies two failure modes, namely the support capacity criterion and the maximum tunnel convergence.