The objective of this work is to prevent damage of the arterial wall, using a theoretical model of hyperelastic, anisotropic, and dynamic behavior of the human arterial. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis in order to understand the effect of the size of the plaque deposit, the loss of elasticity of the wall, and the increase in the density of the blood on the mechanical behavior of the human arterial wall. The great contribution of this work shows us that increasing the size of the plaque also increases arterial stress, and the radial growth of the plaque is very dangerous compared to the longitudinal growth. Furthermore, atherosclerosis promotes the loss of elasticity of the arterial wall and increases the density of blood mass. Indeed, all these subsequent phenomena increase arterial stress. All the results are in good agreement with the expected result of the literature and could play an important role in the diagnosis of the patient with an arterial injury. It will also help the doctor and the surgeon to make a good clinical decision and good treatment planning.