Abstract: The key to analyzing the fatigue life of a random vibration system is to determine its stress power density spectra (SPDS) at the fatigable position of load bearing components. A method called unit stress matrix method is proposed in this paper to calculate the SPDS of non-self-vibration components in a random vibration system. The existence of the unit stress matrix is discussed. An example is presented to show the effectiveness of the proposed method and the procedure of calculation.