In this paper, numerical simulations are performed on the lock-in phenomena of vortex induced vibration(VIV) of a two dimensional cylinder. A deforming grid as well as a rigidly moving grid are used to simulate the movement of the cylinder. The grid deformation is accomplished by the linear spring analogy. Converged solutions, which are obtained by controling the grid size and the non-dimensional time step, are used for comparison and validation of the analysis results. Moreover, the efficiency and the accuracy of the coupling methods for fluid-structure interaction are examined.