AbstractOxygen transport from the lungs to peripheral tissue is dependent on the affinity of hemoglobin for oxygen. Recent experimental data have suggested that the maximum human capacity for oxygen uptake and utilization (V̇O₂max) at sea level and altitude (~3000 m) is sensitive to alterations in hemoglobin‐oxygen affinity. However, the effect of such alterations on V̇O₂max at extreme altitudes remains largely unknown due to the rarity of mutations affecting hemoglobin‐oxygen affinity. This work uses a mathematical model that couples pulmonary oxygen uptake with systemic oxygen utilization under conditions of high metabolic demand to investigate the effect of hemoglobin‐oxygen affinity on V̇O₂max as a function of altitude. The model includes the effects of both diffusive and convective limitations on oxygen transport. Pulmonary oxygen uptake is calculated using a spatially‐distributed model that accounts for the effects of hematocrit and hemoglobin‐oxygen affinity. Systemic oxygen utilization is calculated assuming Michaelis–Menten kinetics. The pulmonary and systemic model components are solved iteratively to compute predicted arterial and venous oxygen levels. Values of V̇O₂max are predicted for several values of hemoglobin‐oxygen affinity and hemoglobin concentration based on data from humans with hemoglobin mutations. The model predicts that increased hemoglobin‐oxygen affinity leads to increased V̇O₂max at altitudes above ~4500 m.