This paper considers wave loads on bottom mounted vertical cylinders in the regime relevant to offshore wind turbine monopiles, examining the higher harmonics of the loading from non-breaking waves which are important in engineering design. Although we consider measurements of total force, our focus is on the moments applied about the seabed which have received much less attention in the literature. We consider an empirical ‘Stokes-like’ model whereby the magnitude of the higher harmonics of force or moment are dependent on the linear force or moment time-series raised to an appropriate power and a fixed coefficient. We compare this representation to high quality wave flume measurements and fully non-linear potential flow simulations. In general we find good agreement for all of the harmonic structure except for the triple frequency component where there are significant discrepancies. We also extend the Stokes-like model and show that harmonics of moments can be robustly predicted from the force harmonic and an appropriate constant moment arm for each harmonic, so a more elaborate calculation is generally not necessary.