The structures associated with the nuclear steam supply system (NSSS) of a pressurized water reactor (PWR) warrant evaluation of various non-stationary loading conditions which could occur over the life of a nuclear power plant. These loading conditions include those associated with a loss of coolant accident and seismic event. The dynamic structural system is represented by a finite element model consisting of significant epistemic and aleatory uncertainties in the physical parameters. To provide an enhanced understanding of the influence of these uncertainties on model results, a sensitivity analysis is performed. This work demonstrates the construction of a computational design of experiment which runs the finite element model a sufficient number of times to train and verify a unique aggregate surrogate model. Adaptive sampling is employed in order to reduce the overall computational burden. The surrogate model is then used to perform both global and local sensitivity analyses.