Structural damage detection using modal properties changes in health monitoring of bridges is important. The main challenge in this direction is that the damage is generally a local event and may not have significant effects on the dynamic responses of the structure at low frequencies. In this paper, for the first time, Modal Strain Energy (DI) and Curvature Damage Factor (CDF) methods have been used to identify the support damage of curved bridges. To do this, firstly, the probable damage caused by the earthquake in the curved bridge supports is determined, and then, using the finite element method, a modal properties of a horizontally curved bridge with a subtended angle of 90° before and after damage is extracted. The Modal Assurance Criterion (MAC) has been used to determine the correlation of the mode shapes. The effect of selective modes on the accuracy of DI and CDF indices is also one of the issues examined. The results show that the bearing damage causes new modes in the bridge. These new modes indicate the existence of support damage. By removing newfound modes using the MAC index and also removing the torsional modes, it can be used with a very good accuracy of the DI and CDF indices to identify support damages.