Vortex induced motion (VIM) can occur on any bluff body (such as buoys, FPSOs, semi-submersibles, Spars and TLPs) exposed to current. VIM is well-acknowledged to have a strong impact on the fatigue life of mooring and riser systems and must be quantified and sometimes mitigated. As part of the effort to numerically investigate VIM response of multi-columns floating platform, we start with the fundamental study of VIM around a square column at low Reynolds numbers (Re), seeking to investigate and accurately simulate the dynamic processes of vortex shedding, transportation and wake interactions with the bluff body and its motion in response. OpenFOAM, an open source CFD toolbox, is used to solve the transient flow pattern around a stationary and free moving square cylinder. A rigorous benchmark of the present simulation against experiments and numerical simulations is demonstrated for both stationary and free moving square cylinders at 60 ≤ Re ≤ 200. The cylinder, with a blockage area of 5%, is mounted on elastic supports for free vibration in both in-line and transverse directions. The effects of grid types and resolutions on the key features of vortex dynamics, vortex induced motion, and the stability of dynamic mesh solver in OpenFOAM are explored. It is found that hybrid unstructured grid has better performance and stability than structured-O grid in OpenFOAM dynamic solver. The effects of mass ratio, spring stiffness and damping on the motion of square cylinder are discussed. It is observed that the phase angle difference between lift coefficient and transverse motion of the cylinder is correlated with mass ratio, spring damping and Reynolds number. An abrupt jump of phase angle difference between lift coefficient and transverse amplitude occurs at Re=76 with mass ratio of 25. The damping effect plays a significant role in the phase angle difference between lift coefficient and transverse amplitude of the cylinder.@en