Compelling evidence shows the association of inflammation with atherosclerosis diseases, one of the leading cause of mortality and morbidity worldwide. Recent research indicated that the inflammatory process of atherosclerotic lesions is involved in the progression of atherosclerotic plaques in specific regions, such as the carotid bifurcation, which represents a risk for ischemic stroke as a result of the interaction between the blood and the plaque. We start modeling using 3D idealized geometry in order to capture the most important features of such interactions. Then, we proceed to a partly patient-specific computational domain representing an atherosclerotic artery. Understanding such interactions is of paramount importance preventing the risk of the plaque rupture. The numerical results comparisons have shown that, qualitatively, there is an agreement between idealized atherosclerotic artery and patient-specific atherosclerotic carotid artery. The idealized carotid geometry will be useful in future FSI studies of hemodynamic indicators based on medical images.