An　analytical　model　for　the　kinematic　response　of　a　single　floating　pile　in　a　two-layered　soil　under　vertically　propagating　P-waves　is　proposed　by　elastodynamics.　A　Heaviside　step　function　is　introduced　to　simulate　the　variability　of　the　layered　soil.　The　continuity　of　the　pile　and　the　fictitious　soil　column　are　considered　based　on　Tajimi＇s　theory.　The　main　contribution　of　the　present　solution　is　that　the　model　of　the　fictitious　soil　column　for　the　floating　pile　in　the　homogeneous　soil　under　vertically　propagating　P-waves　is　extended　to　the　two-layered　soil　with　the　simulation　of　the　depth-dependent　soil　mode　function.　The　effect　of　the　properties　of　the　soil　layer　and　the　shaft　on　the　vibration　of　the　soil–pile　system　is　investigated.　For　the　soil　with　the　upper　softer　layer,　the　dimensionless　cutoff　frequency　of　the　two-layered　soil　is　smaller　than　that　of　homogeneous　soil　and　the　opposite　trend　is　for　the　soil　with　an　upper　stiffer　layer.　For　the　soil　with　upper　stiff　and　lower　soft　layers,　the　axial　pile　strain　decreases　with　the　decrease　of　the　soil　modulus　ratio　and　the　effect　of　soil　modulus　ratio　on　the　soil　resistance　at　the　lower　part　of　the　shaft　is　negligible.　©　2023　Elsevier　Ltd