Purpose: Connecting outflow cannula of LVAD to the aorta is an underexplored issue but may have considerable impact. In fact the hemodynamic modifications due to implantation in this region can cause thromboembolic events. It is therefore important to understand the flow pattern in this region and the way device interacts with the cardiovascular system. We present here the mathematical settings and results of a numerical model of the anastomosis between the outflow cannula of LVAD and the aorta. Methods: The geometry of the aorta and that of nearby large arteries is obtained from MRI and CT-scan data. The geometry of the arterial wall and that of the cannula is obtained by extruding the fluid surface based on a relation between wall thickness and local radius. Simulations are run using the parallel Finite Element library LifeV, which can address 3D Fluid Structure Interaction (FSI). The interaction with the entire cardiovascular system is modeled by using a multiscale model. The latter allows the coupling between the 3D model and a 1D tree model of the rest of the cardiovascular system. Results: Our numerical model allows the understanding of the behavior of the blood flow near the anastomosis and the interaction between LVAD and the cardiovascular system. Besides, relevant parameters from the haemodynamical standpoint are identified in order to propose a general mathematical approach to identify an optimal configuration of the anastomosis between LVAD and aorta. Summary: Mathematical settings and results of a numerical model of the anastomosis between the outflow cannula of LVAD and the aorta.