We consider the risk of high level radioactive waste from nuclear power plants, once buried in the ground, being released by ground water intrusion and eventually being ingested by a human to cause cancer. A probabilistic risk analysis is given for an average United States burial site—it seems reasonable to assume that a particular carefully selected site would be at least as secure. If the effects are summed indefinitely into the future, the result is 0.02 deaths per gigawattelectric year (GWe -y). It is shown that this is thousands of times less than the deaths per GWe-y now being caused by coal burning electricity generation. Compelling arguments are given that only effects over the next 1,000 years should be considered, and these are very much smaller. A probabilistic risk analysis is given for an average low level waste burial site, adding up effects indefinitely into the future; the result is 0.0005 deaths per GWe-y . The reasons why the public perceives the dangers from radioactive waste to be so m...