A method of performing probability calculations for nuclear-reactor surface temperatures has been devised. The method gives consideration to the fact that some uncertainties may vary systematically over all the reactor or over some parts of it. The method does not depend on assumption of any particular form of the probability distributions. The method was used to do an example calculation for an MTR-type test reactor with plate-type fuel elements. It was shown that the calculated probability of failure, that is, that surface temperature exceeds coolant saturation temperature, lies closer to values obtained from the Deterministic Method than to values from the Statistical Method. The calculated probability value was identified as the probability of success at the instant of reactor startup. It was observed that the probability of success for continued operation might not be the same as the value for startup. The method gives an improved representation of the probability problem for reactor surface temperatures. However, there is still much to be learned about the various important distribution functions. In the present situation of inadequate knowledge of behavior and distributions of uncertainty factors, all such probability calculations must be regarded as providing only a rough approximation to the true probability of success for a reactor.