The move from conceptual design, through fabrication to observation and measurement on the resulting physical structure is fraught with uncertainty. This, together with the necessary simplifications inherent when using the finite element technique, makes the development of a predictive model for the physical structure sufficiently approximate that the use of random structural models is often to be preferred. In this paper, the random uncertainties of the mass, damping and stiffness matrices in a finite element model are replaced by random matrices, and a highly efficient pseudo excitation method for the dynamic response analysis of non-parametric probability systems subjected to stationary random loads is developed. A numerical example shows that the dynamic responses calculated using a conventional (mean) finite element model may be quite different from those based on a random matrix model. For precise fabrication, the uncertainties of models cannot be ignored and the proposed method should be useful in the analysis of such problems.