Transuranic solid waste that has been generated as a result of the production of nuclear material for the United States defense program at the Savannah River Site (SRS) has been stored in more than 30,000 55-gallon drums and various size carbon steel boxes since 1953. Nearly two thirds of those containers have been processed and shipped to the Waste Isolation Pilot Plant. Among the containers assayed so far, the results indicate several drums with fissile inventories significantly higher (600-1000 grams {sup 239}Pu) than their original assigned values. While part of this discrepancy can be attributed to the past limited assay capabilities, human errors are believed to be the primary contributor. This paper summarizes an assessment of the probability of occurrence of a criticality accident during handling of the remaining transuranic waste containers at SRS.