Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. We hypothesize that the problem of vascular patterning is ‘solved’ by over-abundant stochastic sprouting angiogenesis in response to a growth factor generated in hypoxic regions (e.g. vascular endothelial growth factor, VEGF), coupled to structural reactions (growth, regression, elimination) of each vessel to mechanical and biochemical stimuli. According to this hypothesis, angiogenesis results in networks with disordered structures, which organize themselves into functional networks through structural adaptation and pruning. To test this hypothesis and analyze the relations between biological mechanisms and system properties, we developed a theoretical model that integrates simulations of network blood flow, convective and diffusive oxygen transport, generation and diffusion of VEGF, stochastic sprouting angiogenesis, structural adaptation and vessel elimination by pruning. The simulation of structural adaptation of vessel diameters includes information transfer by conducted responses along vessel walls, which is needed for proper flow distribution and avoidance of functional shunts. The model is based on experimental observations of network structure and hemodynamics in rat mesentery, a thin sheet-like tissue. The model results show that the combination of stochastic angiogenesis stimulated by a growth factor, structural adaptation and pruning in response to hemodynamic and metabolic stimuli is capable of solving the ‘problem’ of vascular patterning and can generate hierarchical networks with low diffusion distances. To establish and maintain such networks, the following mechanisms are essential: (i) generation of a diffusible vessel growth factor in hypoxic tissue regions; (ii) formation of vessel sprouts in response to above-threshold levels of growth factor; (iii) maintenance of sprouts without pruning before they connect to other vessels; (iv) ability of sprouts to connect with other vessels forming patent flow pathways; (v) diameter adaptation of flowing vessels to hemodynamic and metabolic stimuli and upstream conducted responses; (vi) elimination of redundant vessels by pruning. The model allows assessment of the roles of individual mechanisms in the patterning process and changes resulting from their modification, as may occur in pathological conditions such as tumor growth. Resulting insights may stimulate further experimental investigations of angiogenesis and development of novel therapeutic approaches.