Considering　both　construction　and　operational　costs,　shallow　cavern　excavation　in　hard　rock　formations　is　a　promising　solution　for　large-scale　compressed　air　energy　storage　(CAES).　In　such　strata,　the　surrounding　rock　is　subjected　to　cyclic　tensile　stress　during　air　injection　and　extraction,　potentially　compromising　long-term　cavern　stability.　This　study　investigates　the　cyclic　tensile　behavior　of　rock　under　varying　maximum　stress　conditions.　The　results　indicate　that　cyclic　tensile　loading　induces　irreversible　plastic　strain,　which　escalates　with　increasing　maximum　tensile　stress.　When　the　tensile　stress　exceeds　a　critical　threshold,　fatigue-induced　tensile　failure　occurs.　To　address　this,　a　nonlinear　constitutive　model　incorporating　fractional　derivatives　was　developed　to　characterize　rock　deformation　under　cyclic　tensile　stress.　The　proposed　model　effectively　captures　the　temporal　evolution　of　tensile　strain　by　accounting　for　changes　in　tensile　stress　and　rock　viscosity.　Parameter　fitting　and　model　validation　reveal　that　the　model　accurately　predicts　rock　deformation　under　cyclic　tensile　conditions,　providing　a　valuable　tool　for　assessing　the　long-term　stability　of　CAES　caverns.　©　2024　Elsevier　Ltd