The optimum number of total capillaries in the whole human body was estimated from the analysis of the efficiency for oxygen (02) transport in the vascular-tissue system. We used a tissue model composed of uniform spheres in which 0 2 diffuses from the capillary located at the centre of each sphere towards the surrounding tissue consuming 0 2 at a constant rate. The tissue mass supplied by a single capillary was estimated as the area of positive O 2 concentration under a given condition of capillary flow and O 2 consumption rate. Total tissue mass was determined as the function of the capillary number n and the total blood flow. On the other hand, the energy cost required to maintain the vascular system with n terminals was assessed by using the minimum volume model (Kamiya and Togawa, Bull. math. Biophys. 34, 431-438, 1972). The efficiency of the entire vascular-tissue system was evaluated by calculating the ratio of total tissue mass/cost function. The result of the calculation using physiological data of cardiac output and O2 consumption for an average human adult during a heavy exercise revealed the maximum efficiency occurring at the capillary number 3.7 x 101ยฐ which coincided well with its normal range of physiological estimates (3.2x 10~ยฐ-4.2x 101ยฐ). We concluded that the entire vascular-tissue system is constructed so as to attain the highest efficiency in O 2 transport at its maximum activity.