The　influence　of　the　vertical　and　horizontal　impedances　of　soil　radial　heterogeneity　was　studied　theoretically　based　on　the　series　convergence　and　transfer　matrix　methods.　The　soil　around　the　pile　was　assumed　to　be　composed　of　two　homogeneous　soil　zones　in　three-dimensional　axisymmetric　space,　that　is,　a　disturbed　inner　boundary　zone　and　an　outer　semi-infinite　undisturbed　zone.　Moreover,　the　shear　moduli　of　the　inner　perturbed　and　the　outer　unperturbed　zones　were　correlated　with　a　specific　parabolic　function.　Then,　the　soil　vertical　and　horizontal　impedances　in　the　radially　inhomogeneous　boundary　zone　were　derived　based　on　the　series　convergence　and　transfer　matrix　methods　using　the　stress　and　displacement　continuity　conditions　and　the　infinite　boundary　condition.　Finally,　the　impedance　errors　and　applicable　range　of　two　methods　are　discussed.　The　main　findings　can　be　categorized　as:　(1)　when　analysing　a　soil　radial　heterogeneous　site,　the　influence　of　the　shear　modulus　ratio　of　the　inner　and　outer　zones,　the　ratio　of　the　thickness　of　boundary　zone　to　the　pile　radius,　soil　density　and　pile　radius　should　be　taken　into　account;　(2)　when　0.8　＜=　G(i)/G(0)　＜=　1.0　and　1　＜=　t(m)/r(0)　＜=　4,　the　error　between　the　series　convergence　method　and　transfer　matrix　method　is　within　10%,　while　the　error　is　approximately　15%　when　0.4　＜=　G(i)/G(0　)＜=　0.7.