Until a long-term solution for the disposal of spent nuclear fuel (SNF) is available, interim dry casks will be increasingly used for the storage of SNF discharged from civilian nuclear power reactors. Dry casks containing commercial SNF may hold several significant quantities of plutonium, so appropriate nuclear material safeguards monitoring is needed. An external remote monitoring system (RMS) has been developed to advance dry cask safeguards monitoring beyond the current method of containment and surveillance used to maintain continuity of knowledge. In this study, neutron transport simulations of SNF assemblies in a dry cask were performed for several special nuclear material diversion scenarios. The simulations considered various loading patterns and fuel storage durations as long as 100 years. For each fuel loading pattern and storage time investigated, the simulation results were used to calculate the required measurement time to achieve a nondetection probability β ≤ 10% for the diversion of any single fuel assembly in the cask. The calculations were performed for false alarm probabilities α as low as 0.0001% (or 10−6). A Monte Carlo postprocessing approach was developed to consider the impact on the required measurement time of uncertainty in the burnup of fuel assemblies. The study found that the external RMS is well suited for the surveillance of SNF in dry cask storage for nuclear safeguards or other purposes and is able to detect the diversion of a single SNF assembly even after decades of storage and with a very low false alarm probability.