Flow-induced plastic collapse of stacked fuel plate assemblies was first noted in experimental reactors such as the ORNL High Flux Reactor Assembly and the Engineering Test Reactor (ETR). The ETR assembly is a stack of 19 thin flat rectangular fuel plates separated by narrow channels through which a coolant flows to remove the heat generated by fission of the fuel within the plates. The uranium alloyed plates have been noted to buckle laterally and plastically collapse at the system design coolant flow rate of 10.7 m/s, thus restricting the coolant flow through adjacent channels. A methodology and criterion are developed for predicting the plastic collapse of ETR fuel plates. The criterion is compared to some experimental results and the Miller critical velocity theory.