Tunnel excavation in squeezing ground exhibits large time-dependent and often anisotropic deformation. Within the context of the Fréjus road tunnel and its safety gallery excavated under the Alps between France and Italy, an interesting configuration of two parallel tunnels under squeezing ground conditions is observed. The special feature of this case study lies in the fact that both tunnels have been excavated in similar geotechnical conditions but with different excavation techniques. The road tunnel was excavated with conventional drill and blast methods in the 70s, whereas the safety gallery was excavated between 2009 and 2016 with a single-shield tunnel boring machine (TBM). This paper presents monitoring data processing and numerical simulations of both tunnels with the aim of studying the influence of the excavation method on the time-dependent tunnel response. A calibration of a visco-elasto-plastic anisotropic constitutive model based on the back-analysis of convergence measurements retrieved during the excavation of the Fréjus road tunnel is carried out. The identified ground behavior can be extrapolated to the parallel zones of the safety gallery. In particular, we are interested in the prediction of the stress state in the segmental lining of the gallery during its excavation and the comparison with in situ measurements. It is shown that the time-dependent behavior of the ground is affected by the excavation technique. Finally, an attempt to predict the long-term response of both tunnels is proposed.