Abstract: The problems of non-stationary random response of stochastic rigid frame structures are studied in this paper. From the expressions of structural stationary random response, the mean value, variance and variation coefficient of the mean square value of the structural displacement and stress response under the non-stationary random excitation are derived by means of the random variable's functional moment method and the algebra synthesis method. The randomness of the structural physical parameters are considered. The influences of the randomness of structural physical parameters on the randomness of the mean square value of the structural displacement and stress response are investigated. Examples are presented to verify the formulations.