The fractional ow reserve (FFR) provides an efficient quantitative assessment of the severity of a coronary lesion. Our aim is to address the problem of computing non-invasive virtual fractional ow reserve (VFFR). In this paper, we present a preliminary study of the main features of ow over a stenosed coronary arterial portion, in order to enumerate the different factors affecting the VFFR. We adopt a non-Newtonian ow model and we assume that the two-dimensional (2D) domain is rigid in a first place. In a second place, we consider a simplified weakly coupled FSI model in order to take into account the infinitesimal displacements of the upper wall. A 2D finite element solver was implemented using Freefem++. We computed the VFFR profiles with respect to different lesion parameters and compared the results given by the rigid wall model to those obtained for the elastic wall one.