A vertical circular cylinder which is in periodic oscillatory motion with small amplitudes in finite depth is considered. The usual assumptions necessary for the potential Row stand valid in the present study. A classical perturbation procedure is employed to solve the nonlinear problem through the second-order. According to the solution method presented, the fluid domain is separated into interior and exterior regions in which boundary-value problems (BVP) are decomposed into two BVPs each having one nonhomogeneous boundary condition. A nonhomogeneous second-order free-surface condition is treated by means of a modified form of Weber's integral theorem. Eigenfunction expansions are used for homogeneous solutions. Thus, to conclude the solution, the exterior and interior solutions are then matched on the common boundary. Numerical results are given for a heaving vertical circular cylinder. Wave field analysis around a vertical cylinder shows that the second-order wave pattern is typically dominated by the second-order wave number related to the second-order dispersion relation. The procedure also satisfies the conditions at infinity through the second-order.