Based on the theory of incremental dynamic mechanics， longitudinal dynamic response of initially homogeneous isotropic saturated soil under the influence of borehole pressure is investigated theoretically. Firstly，the radial inhomogeneity of soil medium is deduced. Then，longitudinal dynamic governing equation of each annular is deduced based on the plain strain assumption. The analytical solution is also arrived. Finally，the influence of inhomogeneous initial stress field caused by borehole pressure on the longitudinal impedance of soil is analyzed，and available solution is presented for a comparison of present solution.