This　paper　proposes　complex　variable　solutions　for　stress　and　displacement　fields　for　tunnel　excavation　at　great　depth　in　a　visco-elastic　geomaterial,　considering　the　equivalent　three-dimensional　effect,　liner　installation,　supporting　delay,　and　the　interaction　between　liner　and　geomaterial.　The　geomaterial　is　simulated　by　three　typical　visco-elastic　models:　the　three-parameter　solid　model,　the　Poyting-Thomson　model　and　the　Burgers　model.　The　proposed　solutions　can　simulate　both　tunnel　excavation　and　liner　installation　stages,　which　are　continuous　in　the　time　dimension.　In　the　derivation,　the　variable　substitution,　the　Laplace　transform,　and　their　inverse　computations　are　applied.　The　proposed　solutions　are　verified　in　detail　by　comparing　to　a　numerical　solution　and　a　set　of　field　data.　Good　agreements　between　the　analytical　solution　and　the　numerical　solution/field　data　are　observed,　indicating　the　validity　of　the　proposed　solutions.　Subsequently,　a　parametric　study　is　performed　to　investigate　the　influences　of　tunnel　geometry　(including　tunnel　size　and　liner　thickness),　material　parameters　of　liner　and　geomaterial　(including　Poisson＇s　ratio,　shear　modulus　and　viscosity　of　both　elements),　tunnel　advance　rate,　and　liner　installation　time　moment　(denoting　supporting　delay)　on　the　stress　and　displacement　fields　in　liner　and　geomaterial.　The　proposed　solutions　may　serve　as　an　alternative　method　for　the　conceptual　and　preliminary　designs　in　tunnel　engineering.　(C)　2020　Elsevier　Inc.　All　rights　reserved.