Vortex induced vibrations (VIV) are highly nonlinear due to three different frequencies involved in the process; fluid force frequency, vortex shedding frequency and oscillation frequency. It is computationally complex to solve such a chaotic fluid flow but recent progress in numerical algorithms, turbulence models and computer capabilities have made it easier to approach the problem with a nonlinear approach. These developments have paved the way to approach the problem with the simple equation of motion of Newton's law and when coupled with URANS, which is a commonly used method in solving problems related to fluid flow, the highly nonlinear problem of vortex induced vibrations become solvable. The existing literature computationally can only handle flows for Re > 10,000 - 12,000 but the numerical methodology adopted in this study furthers this limitation. The numerical algorithm is first tried for a stationary cylinder and the boundary layer separation is investigated for higher Re . The generated results are found to be satisfactory to proceed solving for VIV at high Re . The solution strategy is tested in a wide range of Reynolds number with different springs and damping coefficients. Satisfactory agreement is found with the experiments for a cylinder in VIV. The shortcomings of the computational work and why these limitations arise are tried to be explained using the experimental results and the existing mathematical models.