Based　on　the　elastic　foundation　beam　theory，the　mechanical　model　for　the　seismic　response　of　the　vertical　shaft　is　established.　The　shaft　primary　lining　and　secondary　lining　are　simplified　as　Euler　Bernoulli　beams　and　the　normal　interaction　between　the　primary　lining　and　secondary　lining　is　simulated　by　using　uniformly　distributed　springs.　The　differential　governing　equations　of　the　shaft　under　the　horizontal　seismic　excitation　are　derived.　The　rapid　solution　of　the　horizontal　seismic　response　of　the　primary　lining　and　secondary　lining　is　achieved　through　the　distributed　transfer　function　method　and　the　correctness　of　the　analytical　solution　is　verified　by　comparison　with　the　finite　element　numerical　simulation　method.　The　peak　seismic　response　at　the　top　of　the　shaft　is　parametrically　analyzed　from　the　perspectives　of　elastic　foundation　stiffness，secondary　lining　stiffness，shaft　outer　diameter，and　stiffness　of　the　elastic　connection　layer　between　the　primary　and　secondary　linings，respectively.　The　results　show　that　the　peak　seismic　response　at　the　top　of　the　secondary　lining　is　greater　than　that　of　the　primary　lining.　With　the　increase　of　the　elastic　foundation　stiffness，the　peak　response　of　the　top　of　the　primary　lining　and　the　secondary　lining　decreases.　The　increase　of　secondary　lining　stiffness　leads　to　the　obvious　increase　of　peak　response　at　the　top　of　secondary　lining.　With　the　increase　of　the　shaft　outer　diameter，the　peak　response　of　both　the　primary　and　secondary　linings　increase　significantly.　When　the　elastic　connection　layer　stiffness　increases，the　peak　response　of　the　primary　lining　increases　slightly，but　the　peak　response　of　the　secondary　lining　decreases　significantly.　©　2024　Nanjing　University　of　Aeronautics　an　Astronautics.　All　rights　reserved.