A utility method is presented and used to calculate the Stokes finite amplitude wave forces on vertical circular cyclinders commonly used in offshore structures. The n+1 order diffracted wave loads may be evaluated by using this method when the n order wave velocity potential is given. A special asymptotic method may simplify the calculation of the nonlinear term integral over infinite free surface. The results of second order diffracted wave forces on an isolated surface piecing vertial cylinder tally with the related experimental data.