A　rigorous　mathematical　model　is　developed　to　analyze　the　kinematic　response　of　monopiles　embedded　in　the　seabed　under　vertically　incident　P-waves.　The　seabed　is　considered　to　consist　of　nearly　saturated　soil,　in　which　the　mixture　of　pore　water　and　dissolved　air　bubbles　is　treated　as　a　homogeneous　fluid　phase.　The　governing　equations　of　soil　and　pile　are　formulated　using　the　Biot＇s　poroelastodynamic　theory　and　one-dimensional　bar　vibration　theory,　respectively.　The　frictional　forces　between　the　inner　and　outer　soil　layers　are　derived,　and　a　closed-form　series　solution　for　the　monopile＇s　vertical　seismic　response　is　obtained　by　applying　the　boundary　conditions　of　the　pile-soil　system.　The　proposed　solution　is　validated　through　comparisons　with　existing　studies　and　is　subsequently　used　to　explore　the　effects　of　key　parameters　and　the　role　of　inner　soil　on　the　seismic　behavior　of　the　soil-pile　system,　leading　to　several　significant　conclusions.　©　2024　Elsevier　Ltd