A parametric study of several parameters relevant to design safety on the spent nuclear fuel (SNF) rod response under a drop accident is presented. In the view of the complexity of interactions between the independent safety-related parameters, a factorial design of experiment is employed as an efficient method to investigate the main effects and the interactions between them. A detailed single full-length fuel rod is used with consideration of post-irradiated fuel conditions under horizontal and vertical free-drops onto an unyielding surface using finite-element analysis. Critical drop heights and critical g-loads that yield the threshold plastic strain in the cladding are numerically estimated to evaluate the fuel rod structural resistance to impact load. The combinatory effects of four uncertain parameters (pellet-cladding interfacial bonding, material properties, spacer grid stiffness, rod internal pressure) and the interactions between them on the fuel rod response are investigated. The principal finding of this research showed that the effects of above-mentioned parameters on the load-carrying capacity of fuel rod are significantly different. This study could help to prioritize the importance of data in managing and studying the structural integrity of the SNF.