The　rigorous　solution　for　the　single　floating　pile　in　layered　soil　subjected　to　lateral　dynamic　loads　acting　on　the　pile　head　is　proposed.　A　unified　depth　-dependent　soil　mode　function　is　systematically　constructed　using　the　matrix　transfer　method　to　ensure　layer　interface　continuity.　The　model　captures　the　pile　head　compliance　comprehensively,　encompassing　swaying,　rocking　and　cross　-swaying　-rocking　compliance　components.　The　model　is　validated　by　comparing　with　the　existing　solutions.　The　cutoff　frequency　for　each　mode　is　obtained　explicitly　and　is　captured　by　the　present　model.　Parametric　studies　show　that　the　cutoff　frequency　for　the　pile　head　swaying　compliance　component　reaches　the　maximum　value　corresponding　to　each　order　of　the　cutoff　frequency.　The　swaying　compliance　is　affected　significantly　by　the　properties　of　the　shallow　layer,　but　its　effect　on　the　rocking　-associated　compliance　components　is　limited.　Furthermore,　the　horizontal　displacement　of　the　pile-soil　system　develops　deeper　and　broader　when　the　stratum　becomes　softer.　The　soil　displacement　attenuates　rapidly　with　the　distance　to　the　pile　and　dissipates　when　it　exceeds　20　times　the　pile　diameter.