Vortex induced vibrations (VIV) for energy extraction have been revisited in last years by both marine power and wind power communities. Even though vortex induced vibrations have been focus of research for many years, energy extraction from vortex induced vibrations is relevantly new field which needs more detailed investigation and modeling. To this end, there has been recent experimental and modeling parametric studies where VIV was modeled by solution of one-degree-of-freedom ordinary differential equation spring system where engineering modeling of vortex induced vibration for energy extraction has been investigated based on a spring system with the forces defined from forced oscillation experiments where full coupling of free oscillations were not taken into account. Herein a Computational Fluid Dynamics (CFD) modeling of a circular cylinder will be studied to compare forced and free vibrations in the context of vortex-induced energy extraction. The model is essentially solved by partial differential isothermal incompressible Navier-Stokes equations to model fully mathematical model of the fluid-structure interaction of vortex induced vibration. The comparison between forced and free oscillation response studies of this paper will serve to improve the scientific knowledge where vortex induced vibration modeling are comparatively more limited. The preliminary results are presented herein for forced and free oscillations for the Reynolds number regimes Re = 100 and Re = 3800 in two dimensions for combinations of amplitudes and frequency of oscillations in the context of energy extraction modeling.