The core support structure of a fast breeder reactor supports the fuel assemblies, supplies sodium coolant to the fuel assemblies, and maintains the insertability of control rods even during an earthquake. The core support structure is designed as a box fabricated of welded plates, ribs, and cylinders that distribute the load in a diverse manner, in order to reduce the weight and to fulfill safety-related functions. This box structure was not adopted in the Monju prototype reactor; thus, a method to evaluate the structural integrity of this structure must be developed. To prepare design guidelines, structural integrity was studied in accordance with the requirements and features of the box structure. This study consisted of the evaluation of crack propagation under loadings on cracks with hypothetical dimensions as well as an ordinary structural design method. To clarify the crack propagation behavior, partial-scale model tests were conducted that simulated typical core support structure parts. From the results of these experiments, the crack growth rate was evaluated and incorporated into the structural integrity evaluation method. Finally, the structural integrity of the core support structure of the Japanese demonstration reactor is evaluated by this method.