Abstarct: Evaluation of interaction between new and existing underground spaces is one of the most important subjects in urban tunneling. In some cases, it is essential to excavate tunnels close to each other that leads to important interaction effects. In this thesis, using 3D numerical modeling of line 1 twin tunnels (Sahand & Sabalan) and line 2 single tunnel of Tabriz subway, deformation pattern of lining of twin tunnels due to excavation of single tunnel with different horizontal distances has been studied. Also, Forces and moments acting on the lining system of twin tunnels due to excavation of single tunnel with different horizontal and vertical distances adjacent to twin tunnels have been examined and safety factor assigned. Excavation stability of single tunnel while excavating adjacent to twin tunnels with different horizontal and vertical distances has also been Studied using sakurai Criteria and In next step, effects of excavation of single tunnel with different horizontal and vertical distances on the surface subsidence that already occurred due to excavation of twin tunnels have been studied. Ultimately, stability of pillar lying between twin and single tunnels in above mentioned conditions has been studied. Results show that excavation of single tunnel with different horizontal distances cause twin tunnels lining to slightly move opposite side and upward. Also, Lining of twin tunnels lining has good stability against forces and moments acting on it due to single tunnel excavation. Single tunnel is stable while excavating with different horizontal and vertical distances. With decreasing horizontal distance, surface subsidence changes in direction to has more effect on surface structures. Ultimately, Results show that in horizontal distance equal to 1.5D (D, Single tunnel diameter), the plastic zones extent through the whole pillar lying between single and twin tunnels