Forced heave and surge motion of axisymmetric vertical cylindrical bodies with flat and rounded bases are simulated using the advanced CFD software STAR-CCM+ where the overset method is used so that the mesh local to the body moves within a stationary outer mesh. Viscous effects generating drag, and also influencing added mass and radiation damping, are determined. The Reynolds-Averaged Navier–Stokes (RANS) equations are adopted with different turbulence closure models and the water surface is captured by the volume of fluid (VOF) method. These results are of basic interest but the main motive is to assess appropriate drag coefficients for use with linear diffraction models of wave energy converters (WEC) and we have particular interest in the multi-body WEC M4. A basic dynamical model is set up so that drag, added mass and radiation damping coefficients may be obtained from the CFD results. Added mass and radiation damping coefficients were also obtained from the potential flow solver WAMIT for comparison. Mesh convergence studies were undertaken and while mesh independence was achieved for total force it was not possible for the very small shear force. In the laboratory a free heave decay test was undertaken without mechanical contact for bodies with rounded bases and the inferred drag and added mass coefficients were very close to those from CFD. Some general observations are possible for motion in heave. For the hemispherical base the drag coefficient is very low for small amplitudes but this increases as amplitude is increased. For the rounded base with a flat central area the is larger and for the wholly flat base it is larger again but with values less than 0.35. For a larger geometric scale (times 32) for the hemisphere and round base cases the are generally somewhat reduced. For surge motion the show less variation and are always greater than heave values by at least a factor of 2 which is indicative of effects due to separation and wake generation.