An　analytical　method　for　analyzing　the　buckling　of　fully　embedded　single　piles　in　an　elastic　medium　is　developed.　The　medium　is　simulated　by　the　modified　Vlasov　foundation　model.　The　governing　differential　equations　of　the　pile　and　the　surrounding　elastic　medium　in　the　soil-pile　system　are　derived　by　the　variational　principle,　which　are　coupled　when　the　pile　buckles.　A　numerical　iterative　procedure　is　introduced　to　obtain　the　buckling　loads　and　the　corresponding　mode　shapes　of　the　pile.　Parametric　study　is　performed　to　investigate　the　effects　of　the　material　properties　of　the　soil-pile　system　on　the　buckling　capacity　of　the　pile.　Numerical　results　show　that　the　medium　stiffness　has　significant　influence　on　the　buckling　mode　when　the　modulus　ratio　of　the　soil　to　the　pile　is　large.　Moreover,　the　effect　of　Poisson＇s　ratio　of　the　soil　on　the　buckling　behavior　of　pile　is　negligible.　©　2017　World　Scientific　Publishing　Company.