The mean arterial pressure (MAP) is relatively invariant across numerous mammalian species despite variation in body mass spanning many orders of magnitude. This suggests that the origin of the MAP-level may be found in structures or circumstances that are invariable among the species, such as the conditions set by the physics of the system. In most instances, the circulatory system per se does not contribute directly to the main function of a given tissue, e.g. force development in muscle tissue. In addition there is a certain metabolic cost of maintaining a distributing system, i.e. of vessel walls and of the blood itself, increasing with the volume occupied by the system. Arguably therefore, distribution systems such as vascular networks, should occupy as little space as possible within the parenchyma. On the other hand, the distribution system must reach within a sufficiently small distance from every point in the tissue to overcome the limitations set by diffusion properties of substances necessary to sustain tissue metabolism. Different networks with vessels of different dimensions can full-fill the latter requirement however, more narrow vessels requires a larger pressure-volume work pr. volume blood delivered to the tissue. Hence, a balance must exist between not occupying to much space on one hand and not requiring too much energy for the pressure-volume work on the other hand. This balance may be central in determining the MAP. Although blood cells are flexible, the smallest vessels, i.e. the capillaries, must have a size that allows for their passage. Given that capillaries has a certain smallest possible diameter and with capillary length and density being set, average capillary flow velocity must have a size ensuring that the diffusion field of the different species satisfies the surrounding tissues. The question is therefore: which perfusion pressure is needed to deliver blood that has a certain flow-velocity in the capillary bed? Obviously this problem does not have a unique solution since an infinity of combinations of different perfusion pressures and different network structures may give rise to a specific capillary flow-velocity. However, if the physics of the system, i.e. capillary dimensions and a “cost” of increasing the volume of the network sets constraints on the network structure, then one of the two unknowns are fixed and perfusion pressure may converge towards a specific level. To access this problem we present a simple network model composed of a large number of individual vessels. Except for the capillaries, whose dimensions are maintained constant, every vessel in the network is allowed to adapt structurally as regards both lumen diameter and wall-thickness. It is required that each vessel adapts dynamically to a disturbance so as to regain a certain homeostatic state. Homeostasis in this regard means the effect on the vessel wall of transmural pressure and luminal flow. The basic vasomotor mechanisms sensitive to these entities are the myogenic response and the flow-dependent mechanism operating via circumferential wall stress and endothelial shear stress respectively. Whereas these mechanisms set the basic level of vascular tone, they are subject to modulation by other mechanisms such as local metabolism and vascular conducted responses. Eventually all mechanisms feed into a common activation function that determines vascular diameter both acutely (through changes in tone) and chronically (through changes in structure). Simultaneously with these processes, perfusion pressure is allowed to change freely. On performing full-scale simulations of the model each vessel eventually settles in a homeostatic state. At this point networks with realistic structural and hemodynamic properties have emanated. Furthermore, the network perfusion pressure eventually settles at a specific value. The present very simple model indicate that perfusion pressure may be determined by structure and diffusion properties at the lowest level of the system, i.e. the capillary bed, and that the upstream resistance network and the downstream venoular network can adapt so as to ensure a sufficient capillary perfusion while each vessel at the same time remain in homeostasis as regards wall stress and activation.