Rotating turbine blades in aircraft gas turbines are subject to high loads which can result in high cycle fatigue (HCF) failure. In order to reduce the vibration of blades, underplatform dampers are widely used to increase the damping by dry friction dissipating the vibration energy. This paper proposes an energy method (EM) for assessing the damping effect of underplatform dampers with the contacts of one cylinder and one flat without calculating the forced response. In this method the characteristic curve of the damping ratio of the damper on the vibration stress of the blade is used to design the damper. The design objective is that the damper can provide an optimal damping ratio on a given range of vibration stress if resonance occurs. This paper proposes a method for calculating the response and the performance plot based on the above characteristic curve to compare with Direct Time Integration (DTI). The effects of parameters such as contact stiffness, modal data and rotation speed, friction coefficient, damper mass on the damping ratio characteristics are analyzed. Based on the allowable vibration stress of the blade, the design process of the underplatform dampers using damping ratio characteristic curve is given. The proposed method is suitable and efficient for situations where the presence of the damper does not greatly affect the mode shape of the blade.