A model has been developed to represent the stresses developed when a molten, glass-bonded brittle cylinder (used to store nuclear material) is cooled from high temperature to working temperature. Large diameter solid cylinders are formed by heating glass or glass-bonded mixtures (mixed with nuclear waste) to high temperature (915 degrees C). These cylinders must be cooled as the final step in preparing them for storage. Fast cooling time is desirable for production; however, if cooling is too fast, the cylinder can crack into many pieces. To demonstrate the capability of the model, cooling rate cracking data were obtained on small diameter (7.8 cm diameter) glass-only cylinders. The model and experimental data were combined to determine the critical cooling rate which separates the non-cracking stable glass region from the cracked, non-stable glass regime. Although the data have been obtained so far only on small glass-only cylinders, the data and model were used to extrapolate the critical-cooling rates for large diameter ceramic waste form (CWF) cylinders. The extrapolation estimates long term cooling requirements. While a 52-cm diameter cylinder (EBR-II-waste size) can be cooled to 100 degrees C in 70 hours without cracking, a 181.5-cm diameter cylinder (LWR waste size) requires 35 days to cool to 100 degrees C. These cooling times are long enough that verification of these estimates are required so additional experiments are planned on both glass only and CWF material.