Abstract: In this paper，first，the motion response of unsaturated free field under symmetrical condition is obtained via operator splitting and variable separation，in which the wave equation of three-phase porous media and the cou-pling of two immiscible fluids (namely water and air) filled in pores are taken into consideration． Then，on the ba-sis of the continuity condition of upper and lower regions as well as the assumption of Winkler's elastic support at the pile tip，the differential equation of pile vibration is deduced，the frequency domain response of the partially-embedded elastic support pile under steady harmonic vibration is theoretically analyzed，and the closed forms of the impedance function of pile top are obtained． Finally，the complex impedance curves of pile top in unsaturated soil are compared with those in saturated soil，and good agreement is found between the theoretical results and the re-sults obtained from the existing boundary element method and the virtual pile method，which means that the theoret-ical derivation is correct． Parameter analysis results indicate that the complex stiffness of pile top significantly de-creases with the increase of extended segment length; and that the pore water contributes to the dynamic behavior only in approximately saturated condition，while the influences of the saturation and the reaction coefficient at soil layer bottom are rather limited．

Key words: unsaturated soil, partially-embedded pile, elastic support, vertical vibration, impedance function