Maritime structures often comprise cylinders of small diameter relative to the prevailing wave length. This paper describes the Direct Forcing Immersed Boundary (DFIB) simulation of the hydroelastic behaviour of a rigid, horizontal circular cylinder in regular progressive waves. Fluid motions are numerically solved by the full Navier-Stokes equations, and the free surface by the Volume-of-Fluid (VoF) method. The Reynolds number Re = 110, Keulegan-Carpenter number KC = 10, Froude number Fr = 0.69 and Ursell number Urs ≈ 12. A single-degree-of-freedom model is used for the elastically mounted cylinder. Velocity profiles for the stationary cylinder case have been successfully validated using experimental results. The frequency response for reduced velocities 4.5 < UR < 5.3 have been compared with theoretical data. Three transverse vibration regimes are identified: lower beating (4 < UR < 4.5); lock-in (4.7 < UR < 4.8); and upper beating (5 < UR < 10) modes. The lower and upper beating regimes exhibit varying amplitude response. The lock-in mode represents the region of fixed and maximum response. The lower beating andlock-in modes have peaks at a common vibration to wave frequency ratio fw = 2. For the upper beating mode, fw = 1, except for UR = 10 when fw = 2.