Neglecting　the　inertial　forces　associated　with　the　relative　acceleration　of　pore　fluid,　this　paper　presents　a　u-p　analytical　solution　of　the　dynamic　impedances　of　a　horizontally　vibrating　pile　embedded　in　a　saturated　soil　layer　whose　boundary　region　is　radially　inhomogeneous.　To　facilitate　the　analysis,　we　further　divided　the　inhomogeneous　boundary　region　into　a　set　of　concentric　annular　sub-region,　and　the　material　properties　of　each　subregion　are　assumed　to　be　constant.　The　impedances　of　radially　inhomogeneous　saturated　soil　are　calculated　by　making　use　of　transfer　matrix　method.　The　present　solutions　are　compared　with　the　existing　u-w　analytical　solution.　The　influence　of　the　shear　modulus,　permeability　coefficient,　soil　porosity,　pile　radius　and　radial　inhomogeneity　on　the　errors　between　u-p　form　and　u-w　form　are　investigated.　Then,　the　applicable　range　of　the　u-p　approximation　is　given.