Normally, tissue O2 uptake (VO2) is set by metabolic activity rather than O2 delivery (QO2 = blood flow X arterial O2 content). However, when QO2 is reduced below a critical level, VO2 becomes limited by O2 supply. Experiments have shown that a similar critical QO2 exists, regardless of whether O2 supply is reduced by progressive anemia, hypoxemia, or reduction in blood flow. This appears inconsistent with the hypothesis that O2 supply limitation must occur by diffusion limitation, since very different mixed venous PO2 values have been seen at the critical point with hypoxic vs. anemic hypoxia. The present study sought to begin clarifying this paradox by studying the theoretical relationship between tissue O2 supply and uptake in the Krogh tissue cylinder model. Steady-state O2 uptake was computed as O2 delivery to tissue representative of whole body was gradually lowered by anemic, hypoxic, or stagnant hypoxia. As diffusion began to limit uptake, the fall in VO2 was computed numerically, yielding a relationship between QO2 and VO2 in both supply-independent and O2 supply-dependent regions. This analysis predicted a similar biphasic relationship between QO2 and VO2 and a linear fall in VO2 at O2 deliveries below a critical point for all three forms of hypoxia, as long as intercapillary distances were less than or equal to 80 microns. However, the analysis also predicted that O2 extraction at the critical point should exceed 90%, whereas real tissues typically extract only 65-75% at that point. When intercapillary distances were larger than approximately 80 microns, critical O2 extraction ratios in the range of 65-75% could be predicted, but the critical point became highly sensitive to the type of hypoxia imposed, contrary to experimental findings. Predicted gas exchange in accord with real data could only be simulated when a postulated 30% functional peripheral O2 shunt (arterial admixture) was combined with a tissue composed of Krogh cylinders with intercapillary distances of less than or equal to 80 microns. The unrealistic efficacy of tissue O2 extraction predicted by the Krogh model (in the absence of postulated shunt) may be a consequence of the assumed homogeneity of tissues, because real tissues exhibit many forms of heterogeneity among capillary units. Alternatively, the failure of the original Krogh model to fully predict tissue O2 supply dependency may arise from basic limitations in the assumptions of that model.