The effects of a collinear current on the diffraction of regular waves around three-dimensional surface-piercing bodies are examined. With the current speed assumed to be small, the boundary-value problem is separated into a steady current problem with a rigid wall condition applied at the still water level and a linear wave propagation problem in the resulting current field. The boundary conditions of the wave propagation problem are satisfied by a time-stepping procedure and the field solution is obtained by an integral equation method. Free surface profiles, runup, and wave forces are described for a vertical circular cylinder in combined waves and a current. The current is shown to affect significantly the steady drift force and runup predictions. Comparisons of the computed wave forces are made with a previous numerical solution involving a semi-immersed sphere in deep water, and indicate good agreement.