<p>Tunnel-type lined rock caverns (LRCs) are a predominant configuration for compressed air energy storage (CAES) in underground storage systems, where anisotropic horizontal in situ stresses and misalignment between the principal stress direction and the cavern axis are commonly encountered. To address the practical engineering demand for optimal axis orientation of LRCs, this study decomposes the three-dimensional (3D) problem into two sub-problems, plane strain and anti-plane shear, and develops an analytical model that accounts for rotation of the principal stress direction. The proposed solution is validated against 3D finite element analyses. Furthermore, a comprehensive evaluation framework is established by integrating failure risk, stiffness-related deformation demand, and axial warping effects, and a multi-objective optimization is performed to determine the optimal axis inclination angle. The results indicate that the optimal angle is highly dependent on the in situ principal stress orientation and can be categorized into three typical regimes, namely the oblique optimal type, the parallel optimal type, and the perpendicular optimal type. The influences of key design parameters of CAES caverns on the distribution of the optimal angle are also systematically investigated. Finally, 3D finite element simulations integrating rock-lining-sealing structural and material nonlinearity further demonstrate the robustness of the proposed conclusions, providing a basis for axis orientation and optimal design of CAES caverns under anisotropic in situ stress field.</p>