To reduce the computational effort using polynomial chaos expansion to predict the dynamic characteristics of structures with several uncertain parameters, hybrid techniques combining stochastic finite element analysis with either deterministic or stochastic model order reduction (MOR) are developed. For the deterministic MOR, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. For the stochastic MOR, a stochastic reduced basis method is implemented in which the structural modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. To demonstrate the computational efficiency of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate randomized by uncertain geometrical and material parameters is examined. Results are compared with both Monte Carlo (MC) simulations and nonreduced stochastic models. Using the reduced models, the effects of the individual uncertain parameters as well as the combined uncertainties on the dynamic characteristics of the plate are examined.