Abstarct: The Bakhtiari dam is located on Bakhtiari River in Lorestan province, 100 kilometers away from Khoram Abad city. For permanent access to the dam crest, excavation of a spiral tunnel is being studied. Other access tunnels branching from this tunnel in different levels into grout galleries are also being considered. Since this tunnel is planned to be used during the dam operation, it is very important to design the support system. Since some parts of the spiral tunnel will be located on near or top of some others, it is mandatory to study stress distribution and displacement in such tunnels in detail. In this study, geological features, regional rock mechanic properties and the spiral tunnel profile are introduced. Then, Two critical sections were identified. After that, modeling and stability analysis are discussed through conducting numerical finite difference method by FLAC3D software. Then, parametric analysis is performed in order to evaluate the effect of parameters on the stability. Also, a sensitivity analysis is performed to evaluate the effect of tunnel geometric properties on the stability of the tunnel. Finally, support system designation is discussed, according to the numerical analysis results. In summary, to fix the problem of instability, a shotcrete support system mixed with wire mesh and rock bolt is suggested for intersections of spiral tunnel and access tunnels. Also, as a result of the interaction tunnels, to prevent the spread of the settlement in upper levels, a shotcrete support system mixed with wire mesh is suggested for parts of the tunnel which are located in the rock group A.