We test the hypothesis that myoglobin is important for O2 supply near the oxidative capacity of muscle. This hypothesis is evaluated with a simple model that incorporates the properties of heart and skeletal muscle tissue taken from steers and horses exercising at their maximum O2 consumption rate. These tissue samples allowed us to set the bounds on oxidative demand and O2 flux from red blood cells to the core of the muscle fiber, to estimate the blood and tissue capacities for O2 diffusion, and to define the capillary blood PO2 driving this O2 flux. A model combining blood convection with tissue diffusion indicates that O2 diffusion alone is insufficient to achieve the measured O2 fluxes in many samples. The myoglobin content of these fibers is significantly correlated with this O2 diffusion limitation and provides sufficient additional O2 flux to meet muscle O2 demand. The presence of myoglobin maintains the PO2 in the fiber core above anoxic levels for the majority of muscles. Thus myoglobin is critical to O2 supply at fluxes near the maximum and prevents anoxia by maintaining PO2 above levels needed to support mitochondrial function.