We deal with a mathematical model of atherosclerosis plaque formation, which describes the early formation of atherosclerotic lesions. The model assumes that the inflammatory process starts with the penetration of low-density lipoproteins cholesterol in the intima, and that penetration will occur in the area of lower shear stress. Using a system of reaction-diffusion equations, we first provide a one-dimensional model of lesion growth. Then we perform numerical simulations on an idealized two-dimensional geometry of the carotid artery bifurcation before and after the formation of the atherosclerotic plaque. For that purpose, we consider the blood as an incompressible non-Newtonian fluid with shear-thinning viscosity. We also present a study of the wall shear stress and blood velocity behavior in a geometry with one plaque and also with two plaques in different positions.