Abstract: Applying the perturbation method, the solution to the second order diffraction potential of Stokes waves by a vertical circular cylinder is obtained under the frame work of potential theory. The whole second order wave pressure and wave forces are calculated. Considering the geometrical characteristic of vertical circular cylinder, two techniques are adopted. One is using the analytical expressions in the whole fluid domain directly. The other is based on the boundary element method using 1/r type Green function in the inner water region combined with the eigenfunction expansions in the outer region. The comparison between the results of these two techniques shows good agreement. It also indicates that the present method is available to the second order diffraction problem for arbitrary three dimensional bodies.