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Stochastic input data brings aleatoric and epistemic uncertainty to the rack seismic analysis. From the synthetic acceleration-time history of the earthquake to the heterogeneous features of the rack system, several sources of uncertainty exist. The manufacturing process itself may produce slight deviations in the dynamic properties and mass distribution of the rack units. Moreover, each unit is loaded with a different number of fuel elements according to the operation needs of the plant. Even the exact clearance spaces between units are hardly inspectable due to radioactive ambiance. Hence, all of these uncertainties propagate across the nonlinear transient analysis and affect the accuracy and robustness of the numerical outputs. This paper carries out a ‘one-factor-ata-time’ parametric analysis of five key input variables: acceleration time-history, rack mass, fuel loading, rack Eigen-frequencies and hydrodynamic masses. This technique examines the impact on the main transient outputs when an analysis parameter is systematically varied while the others remain at their nominal value. Numerical results are provided for a simple two-rack system as a source of insight into the uncertain seismic response of a real rack system. It is highlighted that the dispersion is much higher for the sliding displacements than for the maximal forces on support.