Maximum horizontal forces by regular waves on a surface piercing vertical cylinder of intermediate scales are computed by solving the two-phase incompressible Navier-Stokes equations with a VOF method. The incident waves are generated by the fifth order Stokes wave and cnoidal wave. The numerical flume is verified and validated by comparison to the second order Stokes theory and by grid-independence. A variety of scales and wave steepness are computed in deep water and finite depth. In fully nonlinear wave condition, the viscosity and diffraction effects are discussed. A more accurate demarcation of intermediate scales is given by scales (the ratio of the diameter to the wavelength) from 0.1 to 0.125.