Successful development, evaluation, and qualification of propulsion systems such as turbojet and turbofan engines and rocket motors require the measurement of the performance and reliability of these systems. Thrust stands or testers are instruments for solid and liquid motors test. In this paper, a method for calculating of solid motors random vibrations effects on a thrust stand structure is developed. At first some Power Spectral Density (PSD) of three kinds of solid motors has been calculated by MATLAB codes. Then a typical thrust stand which has been designed based on special dynamics principles, has been modeled in Solidworks and transferred to ANSYS. In ANSYS, the structure has been analyzed modal and spectral. Then each motor's PSD has been applied on structure separately and maximum stress has been determined by ANSYS codes. Fallowed by structure fatigue life has been estimated by a formula derived from compound of Miner's cumulative fatigue damage ratio equation and Gaussian distribution curve. Results showed amount of PSD at first frequencies has more effect on structure fatigue life and just based on maximum motor thrust can not come to a definite conclusion about the vibrations effects.