The material of piles was assumed as one of the nonlinear elastic materials, which obeys a thrice nonlinear constitutive relation, and the pile was located on an elastic foundation. Following Timoshenko theory of beams and the Hamilton variational principle, a mathematical model of dynamic behavior analysis of nonlinear elastic piles was established, in which three displacements and two angles were contained. As application of the model, the axial movement and the plane coupling movement of nonlinear elastic piles were computed by using the finite difference method and Newton-Raphson iteration method. The corresponding numerical solutions were presented. The effects of the nonlinear elastic properties on the structural dynamic response were considered.