Assuming that the materials of the pile and the soil around the pile comply with nonlinear viscoelastic constitutive relation, the partial differential equation governing the lateral vibration of piles was firstly derived. In the case that the viscous characters of materials of the pile and the soil are weak without consideration of nonlinear factors，the exact solution of the equation has been obtained, with boundary condition of one end fixed, the other free in axial direction and hinged support in lateral direction, by the complex model method. Numerical example is given. As a result, it is found that the bigger the rigidity of soil, the bigger the natural frequency of pile； and that the bigger the load on the top of pile, the smaller the natural frequency of pile. The bearing capacity is largely improved because of the existence of soil around pile, the hard soil is more effectively improving the bearing capacity of pile than the soft soil.