Because most spent nuclear fuel storage casks have been designed for low burnup fuel, a safety-significant high burnup dry storage cask must be developed for nuclear facilities in Korea to store the increasing high burnup and damaged fuels. More than 20% of fuels generated by PWRs comprise high burnup fuels. This study conducted a structural safety evaluation of the preliminary designs for a high burnup storage cask with 21 spent nuclear fuels and evaluated feasible loading conditions under normal, off-normal, and accident conditions. Two types of metal and concrete storage casks were used in the evaluation. Structural integrity was assessed by comparing load combinations and stress intensity limits under each condition. Evaluation results showed that the storage cask had secured structural integrity as it satisfied the stress intensity limit under normal, off-normal, and accident conditions. These results can be used as baseline data for the detailed design of high burnup storage casks.