In view of the low permeability and good damage self-healing properties of rock salt, salt caverns are thought to be ideal media to hold natural gas. However, widely distributed salt formations in China were formed bedded by lacustrine sedimentation with significant sedimentary rhythm characteristics. The various interlayers in bedded salt formations may cause instability of the cavern pillar due to their uncoordinated deformation, thus threatening the safety of the whole gas storage caverns. Combining theoretical analysis and numerical simulation, the influence of different characteristics of interlayers on the stability of salt cavern pillars were detailed analyzed. Some main conclusions were summarized as follows: 1) In a sedimentary rhythm, the rock salt and the soft interlayers can be considered as one category, and the hard interlayers can be treated as another category. Compared with the hard interlayers, rock salt and the soft interlayers contributes more to the shrinkage of salt cavern; 2) With the decrease of pillar width or the increase of operating time, the principal stress curves (both σ₁ and σ₃) in the interlayers along the line between the centers of the two caverns generally experience the process of "Bimodal type - Saddle type - Unimodal type"; 3) The entire plastic zone expansion process in hard interlayers of the cavern pillar shows the periodic law of "interfaces - middle interlayer - interfaces - middle interlayer"; 4) As to site selection of salt caverns for gas storage, bedded salt formations with too many interlayers should be avoided. If the interlayers cannot be avoided, the salt cavern should be constructed with interlayers located far away from the cavern center.