This paper presents an analytical method for determining the steady state response of blade with dry friction damper. A complete vibration cycle is divided into four successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined by using analytical solution forms. An analytical solution of the system periodic motion can be formed by combining the four intervals’ solutions. Numerical simulation shows that there are two response peaks in passage through the resonant frequencies of the system without the friction damper and with the friction damper fully stuck respectively. The amplitude of the first peak can be reduced up to 90% by adjusting the value of normal pressure force between the damper’s contacting surfaces. Whereas to determine the optimum pressure force, reduction of amplitudes of two peaks should be considered together.