A two-dimensional transient freezing model is developed to study the dynamics of solidification of a fluid flowing in a cylindrical channel, the walls of which are cooled below the freezing temperature of the fluid. The model is applied to the case of molten fuel flowing downward through the coolant channels in the lower shielding structure of current liquid-metal fast breeder reactor designs subsequent to a hypothetical core meltdown accident. The results indicate that under postaccident conditions, a high potential exists for rapid relocation of significant quantities of core debris across the shield structure.