A　circular　tunnel　in　a　homogeneous　infinite　ground　subjected　to　a　vertically　incident　shear　wave　with　an　arbitrary　vibration　direction　in　the　horizontal　plane　is　considered　in　this　study.　A　simplified　analytical　solution　with　explicit　formulations　for　the　deformation　and　stress　of　the　tunnel　lining　is　presented　here.　The　superposition　of　two　solutions　under　SH　and　SV　waves　are　derived　first.　In　the　analytical　solutions,　the　tunnel　lining　is　taken　as　a　thick-walled　cylinder,　which　enables　more　precise　forecasts　and　is　much　closer　to　practical　engineering　than　the　thin　shell　model　adopted　in　other　previous　solutions.　Moreover,　the　analytical　solutions　consider　the　slippage　effect　at　the　ground-lining　interface　by　introducing　a　spring-type　flexibility　coefficient　into　the　interaction　force　displacement　relationship.　The　results　of　the　analytical　solutions　are　verified　by　a　comparison　with　the　results　of　the　dynamic　numerical　solutions　via　a　3-D　ground-lining　interaction　model　under　earthquakes;　the　results　show　good　agreement.　By　using　the　analytical　solutions,　the　effects　of　the　vibration　direction,　ground　condition,　lining　thickness　and　flexibility　coefficient　on　the　seismic　response　of　the　tunnel　are　investigated.　Additionally,　the　appropriate　range　of　seismic　wavelengths　for　the　analytical　solutions　is　discussed.　The　proposed　solutions　can　be　applied　to　the　seismic　analysis　and　design　of　tunnel　structures.