Compressed air energy storage (CAES) is attracting attention as one of large‐scale renewable energy storage systems. Its gas storage chamber is one of key components for its success. A successful utilization of an abandoned coalmine roadway depends on the stability of the gas storage chamber. The chamber is a multilayer structure and the redistribution of the stress and displacement in each layer is critical to the chamber stability. So far, this redistribution mechanism under any lateral pressure coefficient and internal air pressure has been unclear and thus a quick and easy evaluation on the CAES chamber stability becomes difficult. In this study, the redistributions of stress and displacement in each layer are analytically solved based on complex variable function theory. First, the stress and displacement in three CAES multilayer structures are obtained under any lateral pressure coefficient and internal air pressure. Then, a comprehensive parameter b1 is obtained to describe the redistribution of stress and displacement in rock mass, lining layer, and grout layer. Its linkage with lateral pressure coefficient, internal air pressure, and material properties is analytically expressed. Thirdly, an analytical expression is obtained for the influence range of internal air pressure on chamber stress. Finally, the role and selection of lining and grouting layers are explored at different lateral pressure coefficient and internal air pressure. It is found that the CAES chamber stability can be effectively and quickly evaluated by these analytical solutions and comprehensive parameters and enhanced by a material with low bulk modulus but high shear modulus.