[en] The state of the vessel steel embrittlement as a result of neutron irradiation can be measured by its increase in the nil ductility temperature (NDT). This temperature is sometimes referred to as the brittle-ductile transition temperature (DBT) for fracture. The life extension of the High Flux Isotope Reactor (HFIR) vessel is calculated by using the method of fracture mechanics. A new method of fracture probability calculation is presented in this paper. The fracture probability as a result of the hydrostatic pressure test (hydrotest) is used to determine the life of the vessel. The hydrotest is performed in order to determine a safe vessel static pressure. It is then followed by using fracture mechanics to project the safe reactor operation time from the time of the satisfactory hydrostatic test. The life extension calculation provides the following information on the remaining life of the reactor as a function of the NDT increase: (1) the life of the vessel is determined by the probability of vessel fracture as a result of hydrotest at several hydrotest pressures and vessel embrittlement conditions, (2) the hydrotest time interval vs the NDT increase rate, and (3) the hydrotest pressure vs the NDT increase rate. It is understood that the use of a complete range of uncertainties of the NDT increase is equivalent to the entire range of radiation damage that can be experienced by the vessel steel. From the numerical values for the probabilities of the vessel fracture as a result of hydrotest, it is estimated that the reactor vessel life can be extended up to 50 EFPY (100 MW) with the minimum vessel operating temperature equal to 85 degrees F