Modeling of nuclear criticality was omitted from performance assessment calculations for the Waste Isolation Pilot Plant (WIPP), a repository for waste contaminated with transuranic radioisotopes, located in southeastern New Mexico, based on arguments of low probability and low consequence. Low-probability arguments are presented here. Guidance provided by the Environmental Protection Agency (EPA) - the regulator of WIPP - allowed either qualitative "credibility" arguments or quantitative probability estimates when screening features, events, and processes such as criticality. Although information to quantitatively evaluate the probability of a criticality event was mostly lacking, qualitatively reasoned discussion of the inability to assemble a critical configuration of fissile material was accepted by the EPA. Specifically, after disposal and prior to an inadvertent human intrusion into the repository, there is no credible mechanism to move radioisotopes (and particularly, fissile material) since only small amounts of brine enter the repository, as adequately demonstrated in calculations over the years. An inadvertent human intrusion (an event that must be considered because of safety regulations) might allow a large pressure gradient to move more brine through the repository, but there is still no credible mechanism to counteract the natural tendency of the material to disperse during transport. Unfavorable physical conditions on concentrating fissile material include low initial solid concentration of fissile material, small mass of fissile material transported over 10 000 yr, and insufficient physical compaction; unfavorable hydrologic conditions include the limited amount of brine available to transport fissile material. Unfavorable geochemical conditions on concentrating the fissile radioisotopes include lack of sufficient adsorption and water chemistry conducive to precipitation.