Time-dependent　characteristics　are　key　factors　for　the　instability　and　safety　in　underground　engineering　projects.　Due　to　geological　structure　and　manual　excavation,　any　rock　mass　is　subjected　to　true　triaxial　stress.　Therefore,　true　triaxial　tests　under　the　monotonous　loading　were　conducted　on　sandstones　first　under　different　intermediate　principal　stresses　along　with　a　constant　pore　pressure　to　simulate　rock　in　situ,　and　subsequently,　the　creep　experiments　were　performed　at　different　stress　proportions　under　corresponding　conditions.　The　experimental　results　show　that　anisotropic　deformation　and　rates　vary　with　stress　levels　and　the　intermediate　principal　stress.　Combined　with　literature　data,　the　lateral　deformation　ratio　of　the　intermediate　principal　strain　(Ε2)　to　the　minimum　principal　strain　(Ε3),　is　closely　related　to　the　reciprocal　of　the　side　stress　ratio　for　instant　and　creep　increments　in　the　penultimate　stage.　The　intermediate　principal　stresses　(σ2)　have　a　significant　effect　on　the　creep　behavior　of　sandstone.　Based　on　the　experimental　results,　a　new　anisotropic　creep-damage　model　is　subsequently　developed,　and　anisotropic　damage　is　defined　based　on　statistical　damage　theory.　The　parameter　values　can　be　obtained　using　the　method　of　Universal　Global　Optimization　(UGO).　The　theoretical　predictions　show　good　consistency　with　laboratory　data　and　field　data,　respectively.　The　model　is　reliably　used　to　simulate　creep　behavior　and　gives　a　good　account　of　the　effect　of　intermediate　principal　stresses.　Therefore,　it　could　provide　a　better　understanding　of　the　long-term　stability　of　engineering　projects.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.　2023.