This　paper　presents　a　mathematical　model　for　the　dynamic　analysis　of　axially　loaded　end-bearing　pile　embedded　in　two-layered　viscoelastic　soil.　The　soil　layers　surrounding　the　pile　are　treated　as　Tajimi-type　continua,　and　the　pile　is　modelled　as　one-dimensional　elastic　rod.　This　allows　obtaining　rigorous,　closed-form　expressions　for　the　dynamic　pile　stiffness　and　the　soil　reaction　acting　along　the　pile　shaft.　Predictions　of　the　model　are　validated　against　independent　results,　to　demonstrate　that　the　simplifications　introduced　in　the　formulation　have　trivial　effect　on　predictions.　The　presentation　concludes　with　an　investigation　on　the　effects　of　two-layered　soil　parameters　on　the　vibration　characteristics　of　end-bearing　piles.　There　we　identify　under　which　conditions　soil　stratigraphy　(and　not　just　average　soil　stiffness)　needs　to　be　considered　in　the　dynamic　analysis　of　piles,　and　provide　recommendations　for　practice.　©　2025　Elsevier　Ltd