In this work we aim to describe both the angiogenesis and the growth of a vascular tumor. In the first part of the thesis, we focus only on the formation of new blood vessels, providing an hybrid model to outline the evolution of pressure, chemicals and endothelial cells, that lead the formation of the nascent vasculature. It is important to underline the fact that, in this framework, we neglect the existence of any cancer cell population and we focus only on the growing network dynamics. On the mathematical point of view, this kind of problem deals with coupling mechanism between the interstitial tissue and the network, because blood and chemicals are allowed to flow across the vessels walls.