Based　on　the　dynamic　Winkler　model　and　fictitious　soil　pile　model　to　consider　the　relative　sliding　at　the　pile-soil　interface　and　the　propagation　effect　of　soil　beneath　the　pile　toe,　respectively,　a　more　rigorous　analytical　model　for　the　vertical　vibration　problems　of　a　floating　pile　is　established.　The　general　solution　for　the　displacement　of　soil　is　derived　by　combining　the　Laplace　transform　and　variable　separation　methods.　Then,　the　vertical　dynamic　solution　of　the　floating　pile　is　obtained　by　introducing　the　pile-soil　interface　condition　and　transfer　function　recursion　method.　Furthermore,　extensive　parametric　analyses　are　performed　to　investigate　the　effects　of　the　stiffness　coefficient　for　the　dynamic　Winkler　model,　the　length　of　the　fictitious　soil　pile,　and　the　inhomogeneity　of　the　soils　and　pile　on　the　vertical　vibration　for　the　floating　pile.　This　indicates　that　the　proposed　analytical　model　provides　a　wider　range　and　more　rigorous　application　for　the　vertical　vibration　problems　of　floating　piles　embedded　in　layered　and　limited　thickness　soils.　Moreover,　the　reduced　form　of　the　obtained　solution　can　also　be　applied　to　investigate　the　corresponding　vibration　problems　of　end-bearing　piles.　©　2022　Elsevier　Ltd