Abstract: Based on the boundary model presented by Novak, the soil around the single pile is divided into two regions: the inner nonlinear viscoelastic region and the outer linear viscoelastic region. Soil nonlinearity can be accounted for approximately by using a reduced shear modulus and an increased material damping ratio. The shear modulus and material damping ratio are in nonlinear relationship with the average strain in the inner zone. By means of equivalent linearization method, the three dimensional soil coupling vertical vibration of single pile is studied, and hence its vertical dynamic impedance function is deduced. The example shows that, for the single pile embedded in nonlinear soil, its vertical dynamic stiffness and damping depend on inner soil nonlinearity, slenderness ratio, pile-soil stiffness relationship, density ratio, material damping and exciting load amplitude.