Employing　Biot＇s　dynamic　equations　and　Novak＇s　thin-layer　theory,　an　analytical　model　for　the　horizontal　vibration　of　a　single　pile　embedded　in　the　radially　heterogeneous　saturated　soil　is　established.　Firstly,　the　frequency-domain　response　of　surrounding　soil　is　derived　by　means　of　the　potential　function,　Laplace　transformation　and　variable　separation　methods.　Secondly,　the　analytical　solution　for　the　horizontal　impedance　of　pile　head　is　deduced　by　combining　the　conditions　of　the　displacement　continuity　and　stress　equilibrium　on　the　soil-pile　interface.　Finally,　the　obtained　solution　is　degenerated　to　validate　its　accuracy　via　independent　comparisons　with　different　existing　solutions.　On　this　basis,　the　effect　of　soil　radial　heterogeneity　on　the　horizontal　vibration　of　an　end　bearing　pile　is　further　discussed　by　conducting　an　extensive　parametric　analysis.(c)　2022　Published　by　Elsevier　Inc.