Analytical　solutions　based　on　the　elastic　foundation　beam　model　for　the　bending　response　of　circular　tunnels　under　longitudinally　propagating　shear　waves　are　studied　considering　the　tangential　contact　conditions　at　the　ground-tunnel　interface.　First,　two　kinds　of　new　analytical　solutions　based　on　Timoshenko　beams　resting　on　Winkler　or　Pasternak　foundations　are　developed　considering　different　contact　conditions　at　the　ground-tunnel　interface.　The　contact　conditions　are　considered　by　introducing　a　spring-type　flexibility　coefficient　in　the　force-displacement　relationship.　Then,　the　new　analytical　solutions,　as　well　as　the　traditional　solutions　using　Euler　or　Timoshenko　beams　on　Winkler　or　Pasternak　foundations,　are　compared　with　the　dynamic　numerical　results.　The　new　analytical　solutions　exhibit　good　agreement　with　the　dynamic　numerical　results　for　different　contact　conditions.　However,　due　to　the　neglect　of　the　tangential　interaction　between　the　tunnel　and　surrounding　ground,　traditional　solutions　are　only　suitable　for　predicting　the　seismic　response　of　tunnels　in　the　full-slip　condition.　Finally,　a　parametric　study　is　conducted　to　investigate　the　effects　of　the　earthquake　frequency,　ground　condition,　lining　thickness　and　contact　condition.　The　proposed　analytical　solutions　can　be　used　to　predict　the　seismic　response　of　circular　tunnels　under　longitudinally　propagating　shear　waves　in　engineering　design.