In this talk I will consider an integro-partial differential system which describes the formation of the tumor-driven blood vessel networks. I will present a result of well-posedeness for this PDE system on a compact domain based on an iterative scheme which linearises the PDE. On the linearised system I will prove existence, uniqueness and a Maximum Principle which will provide an uniform bound for the iterative scheme in $L^\infty$. Then I will consider the convergence of the iterative scheme to the original system. In the end I will present a finite difference scheme to approximate the solution, proving a discrete Maximum Principle which will guarantee the stability of the scheme.