This paper presents the mass, concentration, and volume required for a critical event to occur in homogeneous mixtures of fissile material and various other geologic materials. The fissile material considered is primarily highly enriched uranium spent fuel; however, 239Pu is considered in some cases. The non-fissile materials examined are those found in the proposed repository area at Yucca Mountain, Nevada: volcanic tuff, iron rust, concrete, and naturally occurring water. For 235U, the minimum critical solid concentration for tuff was 5 kg/m3 (similar to sandstone), and in goethite, 45 kg/m3. The critical mass of uranium was sensitive to a number of factors, such as moisture content and fissile enrichment, but had a minimum, assuming almost 100% saturation and >20% enrichment, of 18 kg in tuff as Soddyite (or 9.5 kg as UO2) and 7 kg in goethite. For 239Pu, the minimum critical solid concentration for tuff was 3 kg/m3 (similar to sandstone); in goethite, 20 kg/m3. The critical mass of plutonium was also sensitive to a number of factors, but had a minimum, assuming 100% saturation and 80-90% enrichment, of 5 kg in tuff and 6 kg in goethite.