Mechanical circulatory support,in particular ventricular assist devices(VAD),has been recently proposed as an alternative to transplantation in the treatment of terminal heart failure in the context of the lack of donors and raising number of patients on the waiting list. Although these systems have proved their efficiency through a rigorous patient selection, the complication rate remains high and experience shows that many of them are related to haemodynamic modifications due to VAD implantation. Furthermore, VAD themselves have been widely studied, while the flow near the anastomosis VAD-aorta is still not well-known, although many complications arise at this site. We present here the mathematical settings and some preliminary results of a numerical model of the anastomosis between the outflow cannula of left ventricular assist devices (LVAD) and the aorta.