Vortex-induced vibration (VIV) of two rigidly connected circular cylinders in side-by-side and tandem arrangements in the cross-flow direction was investigated using two-dimensional (2D) numerical simulations. The 2D Reynolds-Averaged Navier–Stokes (RANS) equations were solved for the flow, and the equation of the motion was solved for the response of the cylinders. Simulations were conducted for a constant mass ratio of 2.5, gap ratios G (ratio of the gap between the cylinders to the cylinder diameter) in the range of 0.5 to 3, and reduced velocities in the range of 1 to 30. The effects of the gap ratio on the response of the cylinders were analyzed extensively. The maximum response amplitude in the lock-in regime was found to occur at G = 0.5 in the side-by-side arrangement, which is about twice that of a single cylinder. In the side-by-side arrangement, the response regime of the cylinders for gap ratios of 1.5, 2, 2.5, and 3 is much narrower than that of a single cylinder, because the vortex shedding from the two cylinders is in an out-of-phase pattern at large reduced velocities. In the tandem arrangement, the maximum response amplitude of the cylinders is greater than that of a single cylinder for all the calculated gap ratios. For the gap ratio of 0.5 in the tandem arrangement, the vortex shedding frequency from the upstream cylinder was not observed in the vibration at large reduced velocities, and the response is galloping.