In relation to burnup credit, three tasks have been carried out at the Japan Atomic Energy Research Institute (JAERI) for establishing the evaluation method of criticality safety for a spent-fuel system, such as storage ponds and transport casks. The first task is to prepare a benchmark database of criticality experiments and nuclide compositions of spent fuels. The database of nuclide composition is formed by data measured at JAERI and data collected from the literature. For the database of criticality experiments, the effective multiplication factor of a spent-fuel assembly has been measured at JAERI. The next task is to develop computer codes. The burnup and criticality codes have been developed and validated by analyzing a large number of benchmarks stored in the aforementioned database. The last task needed to establish the methodology in order to confirm the subcriticality of a spent-fuel system applying burnup credit is described. A reference fuel assembly is introduced so that the criticality of a system can be evaluated by using it, instead of modeling all fuel assemblies explicitly. To determine the nuclide composition of a spent fuel, a simple method is studied utilizing a large number of nuclide composition data stored in the database. Further, the effects of the axial burnup profile and calculation errors are discussed, and the remaining tasks are identified.