The probability has been estimated for a sudden release of cryogenic hydrogen from the cryogenic hydrogen circulating system into the reactor building of the High Flux Isotope Reactor. Experience data for cryogenic transfer line failures in laboratory settings was obtained from several research facilities around the world. Results (with uncertainty) were obtained by using the Monte Carlo Equation option in the Data Module of the Riskman� probabilistic risk assessment software, yielding a mean of 4.25E-05 per year with a 5th percentile of 6.13E-6 and a 95th percentile of 1.16E-4 per year. Point estimates are included in the report for clarity. The dominant contributors to the likelihood of a release of hydrogen inside the reactor building are design basis (or beyond) seismic events and the probability of a failure in one of the three Johnston couplings inside the shield tunnel. The dominant contributor to the conditional probability of hydrogen being released from the transfer line is common cause failure of the vacuum and helium blanket relief valves. When the seismic risk is removed, the remaining probability of releasing hydrogen in the building is approximately 2.6E-06 per year (point estimate) with the dominant contributor being Johnston coupling failure in the shield tunnel.