This work compares the application of Gaussian orthogonal ensemble statistics for the stochastic free vibration of structures with uncertainties. Two dynamic systems are examined corresponding to a simply-supported plate in flexural motion and a multi-degree of freedom system comprised of mass-spring oscillators coupled in series. For the plate, structural uncertainty was generated by mass perturbations. The mass-spring chain was randomised in two ways. In the first case, every individual mass was modified using a log-normal distribution. In the second case, small mass-spring systems were added at random locations to the main masses. The natural frequencies and frequency statistics are derived for each system. The probability distributions of the modal spacings are presented.