Carotid artery is the major blood vessel which carries oxygenated blood to the brain and the face. Atherosclerosis is a major arterial disease characterized by a progressive contraction of the blood vessel. It occurs due to the deposition of cholesterol and lipids beneath the internal layer of the artery which is called stenosis. Carotid artery stenosis causes serious implications which considered one of the leading causes of morbidity and mortality in most countries. The existence of stenosis had a significant effect on the blood flow dynamic factors. Adding the arterial wall response through the wall elasticity will achieve more accurate and realistic flow characteristics. In this study, the arterial wall elasticity through two-way Fluid-Structure Interaction (FSI) was considered to the developed model to calculate the blood flow dynamics. Moreover, blood dynamic factors will be used to investigate the flow characteristics with rigid and elastic arterial wall and temporal blood responses. To estimate the blood dynamic factors, a three-dimensional reconstructed patient-specific carotid artery geometry with realistic boundary conditions is considered. Hence, a three-dimensional comprehensive model including the non-Newtonian Carreau blood flow viscosity model under pulsatile flow conditions is developed. The two-way FSI procedure was performed by applying an arbitrary Lagrangian-Eulerian (ALE) formulation to calculate the arterial response. Results indicated that using FSI has a crucial role in investigating the blood flow dynamic factors which resulted in low shear stress, pressure gradient, and velocity distribution comparing to the rigid arterial wall response. The efficient use of Computational Fluid Dynamics (CFD) has the potential to shed light on the assessment of the stenosis severity by adding the arterial wall and temporal blood response to the developed model.