Angiogenesis, the formation of new blood vessels from existing vasculature, is the basis of organ growth and repair in healthy conditions and of pathological developments such as cancerous tumors. Consequently, studying mathematically this complex and multiscale fenomena has become more important in the last years. In this talk, we will present a cell-based model structured in terms of multiple scales by incorporating extracellular and cellular levels as well as the results of simulations. We will start with an explanation concerning the theoretical model through its multiple scales and their coupling. We consider chemotaxis and durotaxis at the extracellular level whereas at the cellular level we consider cell migration, growth, proliferation, cellular adhesion, distinction between tip and stalk phenotypes, sprout branching and anastomosis. Coupling between extracellular and cellular levels are considered in a model that incorporates biomechanical and biochemical mechanisms and allows to simulate vessel branching based on purely biological properties. Due to the complexity of this biomathematical model, getting a optimized program to perform simulations has been an important issue. Therefore, the next point in this talk is how to deal with the simulation issue and the role of parallel computation. We will finish this talk showing the simulation results and presenting our future goals.