For　the　aim　to　analyze　the　vibration　characteristics　of　a　single　pile　surrounded　by　radially　inhomogeous　soil,　a　simplified　mechanical　model　for　vertical　vibration　of　a　single　pile　embedded　in　a　radially　inhomogeneous　viscoelastic　soil　is　proposed　by　employing　the　viscous　damping　and　three-dimensional　axisymmetric　continuum　model　with　annular　transferred　complex　stiffness.　Firstly,　the　complex　stiffness　at　the　interfaces　between　soil　and　pile　is　derived　using　Laplace　transform　and　complex　stiffness　transfer　method.　Secondly,　an　analytical　solution　for　dynamic　impedance　at　the　pile　head　is　obtained　by　using　the　compatibility　condition　of　pile　and　radially　inhomogeneous　surrounding　soil.　Furthermore,　the　obtained　analytical　solution　for　dynamic　impedance　at　the　pile　head　is　reduced　to　verify　its　validity　by　comparison　with　an　existing　solution.　Extensive　parametric　analyses　are　performed　to　investigate　the　effects　of　the　parameters　on　the　vibration　characteristics　at　pile　head.　The　computational　results　show　that　the　viscous　damping　coefficient　and　the　damping　factor　only　have　significant　influence　on　the　amplitude　of　dynamic　impedance　at　pile　head,　while　the　stiffness　factor　has　significant　influence　on　the　amplitude　and　resonance　frequency　of　dynamic　impedance　at　pile　head.　The　higher　the　degree　of　softening　(hardening)　of　the　surrounding　soil,　the　larger　(smaller)　the　amplitude　of　the　dynamic　impedance　at　pile　head.　The　larger　the　range　of　softening　(hardening)　of　the　soil　around　the　pile,　the　higher　(lower)　the　level　of　the　dynamic　impedance　at　pile　head.　However,　the　influences　of　the　degree　of　softening　(hardening)　of　the　soil　around　the　pile　and　the　range　of　softening　(hardening)　on　the　resonance　frequency　of　the　dynamic　impedance　at　pile　head　can　be　neglected.　©　2019,　Science　Press.　All　right　reserved.