Within the framework of soil–pile interaction, a novel displacement scheme for the transverse kinematic response of single piles to vertically propagating S waves is proposed on the basis of the modified Vlasov foundation model. The displacement model contains a displacement function along the pile axis and an attenuation function along the radial direction. The governing equations and boundary conditions of the two undetermined functions are obtained in a coupled form by using Hamilton's principle. An iterative algorithm is adopted to decouple and solve the two unknown functions. In light of the governing equation of the pile kinematics, a mechanical model is proposed to evaluate the present method on a physical basis considering material damping. The coefficient of the equivalent Winkler spring is derived explicitly as function of the displacement decay parameter γ and soil Poisson's ratio. A parametric study is performed to investigate the effects of the soil–pile system properties on the kinematic response of single piles. The results show that the dimensionless pile length controls the transverse kinematics of piles. In terms of the theory of beams on elastic foundation, the classification limits of the dimensionless pile length may be π ∕ 4 and π, respectively. Copyright © 2014 John Wiley & Sons, Ltd.