The problem of hemodynamics in a coronary vessel with stenosis is considered, taking into account different boundary conditions on the vessel wall. Two types of conditions are considered: no-slip and slip. The blood model is considered as a non-Newtonian fluid, the viscosity of which is determined using the Carreau model. It is shown that changing the boundary conditions on the slip entails changing the confined fluid flow which leads to significant changes in the hemodynamic pattern throughout the stenosis area up to atypical in-vivo observations. Thus, the choice of the slip boundary condition on the vessel wall,as well as the details of the flow in the near-wall layer, is a key factor in obtaining reasonable results.