Abstract: The layout of parallel tunnels is adopted in many tunnel construction due to the limited space of traffic corridor. The adjacent tunnels with a small clear spacing distance may cause significant interaction to reduce the stability of the surrounding rock. The problem is simplified as the stability model for the parallel multi-line tunnels with equidistance under plane strain. The systematic analysis is carried out using the upper bound method for rigid body translational motion elements. The curves for the stability coefficient of surrounding rock of tunnels the and the failure mode of slip line network under the instable critical state are obtained. The stability of the surrounding rock and the potential failure mode varying with strength parameters, tunnel buried depth H and clear spacing distance of multi-line tunnels S are discussed. The results of the parallel multi-line tunnels are compared with those of the twin-line tunnels reported by the existing literature. It is shown that when the clear spacing distance S is greater than the conversion distance S_tr, the failure mode of a single tunnel is presented for the both types of tunnels, and the stability coefficient N_cr is more consistent. In contrary, when the clear spacing distance S is small, the collapse of the middle rock column caused by the settlement in the whole upper part of tunnels is presented in the surrounding rock of the parallel multi-line tunnels. The stability of the parallel multi-line tunnels greatly decreases compared with the case in the twin-line tunnels. The results may provide data support for evaluation of the stability of the surrounding rock and formulating the reinforcement scheme for the parallel multi-line tunnels.