As a basic study to establish an analytical method about dynamic behaviours of various kind of pile structures and to clarify their characteristics of dynamic response to waves, a theoretical solution has been derived about the vibrations of a small diameter pile due to small amplitude waves. The solution presented here is more concise than the methods of numerical analysis, whereas the integral constants contained in this solution must be determined to satisfy the boundary conditions according to each situation. This paper treats the vertical pile both elongated from the bottom to the water surface and pierced the water surface. For the latter case, the validity of this solution has been verified by comparing the experimental data of the displacement.