We simulate the flow past smooth and rough rigid circular cylinders that are either bare or outfitted with helical strakes. We consider operating conditions that correspond to high Reynolds numbers of 105 and 106, and allow for two degree-of-freedom motions such that the structure is allowed to respond to flow-induced cross-flow and in-line forces. The computations are performed using a parallelized Navier–Stokes in-house solver using overset grids. For smooth surface simulations at a Reynolds number of 105, we use a Smagorinsky large eddy simulation turbulence model and for the Reynolds number cases of 106 we make use of the unsteady Reynolds-averaged Navier–Stokes equations with a two-layer k-epsilon turbulence model. The rough surface modifications of the two-layer k-epsilon turbulence model due to Durbin et al. (2001, “Rough Wall Modification of Two-Layer k-Epsilon,” ASME J. Fluids Eng., 123, pp. 16–21) are implemented to account for surface roughness effects. In all our computations we aim to resolve the boundary layer directly by using adequate grid spacing in the near-wall region. The predicted global flow parameters under different surface conditions are in good agreement with experimental data, and significant vortex-induced vibration suppression is observed when using helically straked cylinders.