A　unified　stress　function　is　represented　in　a　Fourier　series　to　capture　the　complex　stress　state　of　an　underwater　shallow　tunnel　perimeter.　The　first-order　unified　stress　function　is　employed　as　stress　boundary　condition　of　the　tunnel　perimeter　(SBCTP)　to　describe　the　non-symmetrical　stress　with　respect　to　the　horizontal　and　vertical　centerlines　of　the　tunnel.　The　mechanical　analysis　model　of　an　underwater　shallow　tunnel　is　established.　Combining　the　complex　variable　theory,　the　elastic　analytical　solution　of　the　stress　and　displacement　are　obtained.　The　rationality　of　the　elastic　solution　is　verified　by　comparing　the　stress　fields　between　the　proposed　method　and　the　finite　element　method　(FEM).　Based　on　the　obtained　elastic　solution,　the　fractional　viscoelastic　solution　is　determined　by　the　correspondence　principle.　The　time-dependent　ground　displacement　are　investigated　considering　the　effect　of　stress　release.　A　series　of　parameter　analyses　are　carried　out　to　discuss　the　ground　vertical　and　horizontal　stress　distributions　under　the　influences　of　SBCTPs.　©　2020　Elsevier　Ltd