A theoretical model is used to predict the consequences of a postulated hypothetical nuclear criticality excursion in a freezer/sublimer (F/S). Previous work has shown that an intrusion of water into a F/S may result in a critical configuration. A first attempt is made to model the neutronic and thermal-hydraulic phenomena occurring during a criticality excursion involving both uranium hexafluoride (UF6) and uranyl fluoride (UO2F2) solution, which is present in the F/S during upset conditions. The model employs point neutronics coupled with simple thermal hydraulics. Reactivity feedback from changes in the properties of the system are included in the model. The excursion is studied in a 10-MW F/S with an initial load of 3500 kg of 5% weight enriched UF6 and in a 20-MW F/S with an initial load of 6800 kg of 2% weight enriched UF6. The magnitude of the fission release determined in this work is 5.93 × 1018 fissions in the 10-MW F/S and 4.21 × 1018 fissions in the 20-MW F/S. In order to demonstrate the reliability of the techniques used in this work, a limited validation study was conducted by comparing the fission release and peak fission rate determined by this work with experimental results for a limited number of experiments. The agreement between calculations and experiments in the validation study is considered to be satisfactory. The calculational results for the hypothetical accidents in the two F/S vessels appear reasonable.