We present a novel computational framework for simulation of intussusceptive angiogenesis to answer some of the questions concerning the mechanisms of the remodeling process. The model relies on mechanical interactions between blood and tissue, includes the structural maturation of the vessel wall, and is controlled by stimulating or inhibiting chemical agents. The model provides a simple explanation for the controlled formation of micro-vessels and bifurcations from capillaries. Detailed hemodynamic and transport properties for oxygen, metabolites or growth factors can be accurately predicted.