This paper quantifies the structural capacity of the transport steps for oxygen, glucose and fatty acids from the blood in capillaries to the cytosol of muscle cells and compares it with maximal rates of oxygen and substrate transport measured in the same animals and reported in the preceding papers of this series. Dogs have relatively more muscle per unit body mass than goats (37 versus 26%), but the maximal rate of oxidation per gram of muscle is still larger in the dog by a factor of 1.55. The maximal rates of substrate supply from the circulation are similar in both species. We predict that these differences in physiological parameters should be matched by proportional differences in structural capacity. We find that capillary volume and surface area are matched to maximal oxygen demand. The rate of vascular substrate supply is proportional neither to the capillary surface area nor to the length of intercellular junctions. The sarcolemmal surface area per gram of muscle is the same in both species. Using the physiological data presented in the companion papers of this series, we have calculated the maximal flux densities of circulatory glucose and fatty acids across the capillary wall and the sarcolemma. We find, for both substrates, that the flux densities across the sarcolemma reach a maximum at nearly the same level and at low exercise intensities in both species. In contrast, the flux densities across the capillary surface and the endothelial junctions are higher in goats than in dogs. We conclude that the capillaries are designed for O2 supply up to maximal rates of oxidation but not for the supply of the substrates (glucose and fatty acids) at the rates required at high exercise intensities. These are limited by the transport capacities of the sarcolemma.