An　analytical　solution　is　developed　to　investigate　the　model　of　simplifying　the　pile-soil　interaction　to　a　spring-damping　system　when　the　horizontal　earthquake　input　or　the　top　of　the　model　is　subjected　to　horizontal　dynamic　load.　Based　on　Euler-Bernoulli　theory,　the　dynamic　equilibrium　equations　of　pile　in　soil　and　air　are　established,　respectively.　Then,　utilizing　the　corresponding　boundary　conditions,　potential　function　decomposition,　and　transfer　matrix　method,　the　analytical　expression　of　impedance　at　the　pile　head　whether　the　horizontal　earthquake　input　or　the　top　of　the　system　is　subjected　to　horizontal　dynamic　load　can　be　presented.　Furthermore,　the　model　of　the　pile-soil　complex　interaction　can　be　simplified　as　a　spring-damping　system　according　to　the　stress　equilibrium　at　the　pile　bottom　in　the　air.　Moreover,　the　rationality　of　the　present　solution　(without　simplification)　is　verified　by　comparison　with　existing　methods,　and　then　the　difference　between　the　present　solution　(without　simplification)　and　the　spring-damping　system　(simplification)　is　also　compared.　Finally,　the　influence　of　the　parameter　variation　in　the　pile　buried　in　the　soil　and　soil　free-field　on　the　simplified　model　are　discussed.　The　research　results　will　be　instructive　for　the　simplification　of　numerical　model　for　pile-soil　interaction.　(c)　2023　Published　by　Elsevier　B.V.　on　behalf　of　Japanese　Geotechnical　Society.　This　is　an　open　access　article　under　the　CC　BY-NC-ND　license　(http://creativecommons.org/licenses/by-nc-nd/4.0/).