Abstract: Based on the elastodynamics,three kinds of infinite elements are proposed in this paper,which are coup-led with FEM to solve axisymmetrical dynamic problems in a semi-infinite layered space. For excitements appliedvertically at the surface of space,numerical results are perfectly agree with analytical solutions,An application of theproposed method is also offered to investigate the dynamic pile-soil interaction and differences between point andtransfer impedances at top of pile,which will be useful in the vibration test for pile integrity.