An efficient formulation for uncertainty propagation analysis of complex structural models is presented. The formulation is based on parametric reduced-order models. Fixed-interface normal modes and interface modes are approximated in terms of a set of support points in the uncertain parameter space. The potential time-consuming step of computing the modes for different values of the model parameters needs to be performed only at the support points. Based on these approximate modes, reduced-order matrices can be updated efficiently during the simulation process associated with the uncertainty propagation analysis. The effectiveness of the proposed parametric model reduction technique is demonstrated by means of two numerical examples.