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A rigorous mathematical model for determining the failure mode of pressurized vessels exposed to localized jet-re impingement during rapid depressurization or blowdown is presented. Accounting for the thermodynamic trajectory of the two-phase hydrocarbon inventory, the method of separation of variables for non-homogenous heat conduction is used to determine the transient radial temperature gradient across the heated section of the vessel wall. The resulting temperature pro le in conjunction with the appropriate vessel geometry stress equations are then used to simulate the transient triaxial thermal and pressure stress yield propagation. Failure is assumed to occur when any of the total stresses exceed the ultimate tensile strength of the vessel wall material. The application of the model to a real cylindrical vessel under localized jet re attack in the vapour space reveals catastrophic failure involving rapid propagation of a tear along the major axis of the vessel wall due to severe thermal stress loading.