Atherosclerotic plaque deposits are common causes of blood flow disruption in the carotid artery bifurcation and the associated fluid mechanics has been extensively studied using Computational Fluid Dynamics (CFD) and Fluid Structure Interaction (FSI). However, the elastic responses of plaques to hemodynamics in the carotid artery bifurcation has not been deeply studied using either of the above-mentioned numerical techniques. In this study, a two-way FSI study was coupled with CFD technique, using Arbitrary-Lagrangian-Eulerian method, to study the biomechanics of blood flow on nonlinear and hyperelastic calcified plaque deposits in a realistic geometry of the carotid sinus. FSI parameters such as total mesh displacement and von Misses stress on the plaque, as well as flow velocity and blood pressure around the plaques, were analyzed and compared to variables such as velocity streamline, pressure and wall shear stress obtained from CFD simulation in a healthy model. The blood flow simulations reveal complete reversed blood flow behavior in the internal carotid artery, ICAs and external carotid artery, ECAs for both cases. In particular, this study suggests that plaques, irrespective of the masses, possess a high yielding response to hemodynamic forces at the attaching edges, while the surfaces are vulnerable to rupture.