Wavy cylinders have been proven effective in controlling the flow and reducing the fluid induced forces. However, the hydro-elastic behavior of a flexibly mounted wavy cylinder remains unclear. The current paper endeavours to present a systematic study of the flow around a spring mounted wavy cylinder mainly at a moderate Reynolds number of 5000, the results of which are compared with a normal cylinder with the same fluid and structural attributions. It is discovered that the wavy cylinder, although almost eliminates the karman vortices in the fixed configuration, shows only limited efficacy on the mitigation of the flow induced vibration in the case of zero structural damping, and the typical initial-upper-lower type response curve is manifested. The hydrodynamic forces of the wavy cylinder also magnify significantly in the flexibly mounted cases during synchronization. Moreover, the phase lag between the lift coefficient and the displacement displays a clear change from 0 at the initial branch to 180 at the lower branch. The association of the 2S and 2P vortex shedding modes to the different branches is also similar to that of the normal cylinder, in which the 2S mode corresponds to the initial branch and the 2P to the lower branch. In general, despite the absence of the primary shedding frequency in the fixed configuration, the flexibly mounted wavy cylinder exhibits many features that is also found in the normal cylinder. This implies that the vortex induced vibration may not be initiated by the karman vortex shedding, and thus may defy the conventional view on the mechanism of the vortex induced vibrations. Additional simulations are performed with non-zero structural damping. It is disclosed that with sufficiently high structural damping, the vibration of the wavy cylinder could be reduced more efficiently than the normal cylinder.