The seismic risk assessment of tunnels is of fundamental importance, given the great role played by this class of infrastructures in urban areas, as well as in interurban transportation networks. It entails the quantitative evaluation of the seismic-induced damages on these underground structures and, in general, the estimation of their resilience during and after earthquakes. Within this context, the paper presents a three-dimensional (3D) numerical investigation of the seismic response of a shallow twin-tunnel crossing a topographically complex area. The numerical study is inspired by the old Alvaro tunnel, located at the toe of the Costa del Canneto slope (Matera, Italy) in the South of Italy. The 3D finite element model is initialized by simulating a realistic tunnel excavation sequence, performed with conventional methods and subsequent tunnel lining installation, within a heterogeneous subsoil deposit, implementing a shear wave velocity profile variable with depth. The soil behavior is described through the isotropic hardening elasto-plastic hysteretic constitutive model HSsmall, while the tunnel lining is modelled using a linear elastic law. The results emphasize the capability of the 3D modelling approach to estimate the distribution of the lining forces along the whole infrastructure, accounting for the complex topographic conditions, the possible interaction between the two tunnels and the multi-directionality of the seismic motion. Moreover, the calculated damage index distribution shows that, depending on the amount of assumed steel reinforcement, (i) the damages are observed on the lining already at the end of the tunnel construction stage; (ii) the occurrence of an earthquake may significantly aggravate the induced-damage distribution.