Tunnel　portals　are　often　located　in　rather　weak　rock.　Also　the　ground　surface　of　tunnel　portal　section　is　often　inclined　to　form　slopes.　These　characteristics　in　engineering　geology　make　this　section　easy　to　be　damaged　during　earthquakes　both　in　slope　and　in　structures.　A　model　with　single　free　surface　slope　is　built　to　analyze　the　dynamic　response　of　portal　section　of　a　mountain　tunnel.　First,　the　theory　of　elastic　wave　propagation　is　used　to　deduce　the　solution　of　free　field　ground　motion　on　the　axis　of　tunnel　under　incident　SH　wave　without　considering　the　existence　of　the　tunnel.　Then,　the　ground　motions　are　putting　on　tunnel　structure,　where　the　3-D　elastic　shell　theory　is　employed　in　order　to　provide　strains　of　the　structure.　The　analytical　solutions　of　the　model　are　verified　by　the　results　of　shaking　table　test.　In　this　way,　the　analytical　solutions　do　not　only　consider　the　amplitude-time-frequency　effects,　but　also　derives　analytical　expressions　of　axial,　hoop　and　shear　strain　distribution　on　tunnel　cross-sections.　These　results　could　be　references　for　seismic　design　of　tunnel　portal　section　in　mountain　tunnels　and　have　positive　effects　on　reasonable　understandings　of　the　seismic　response　characteristics　in　this　section.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.