Simulations of the behavior of blood vessels were performed, using ANSYS Inc. software, modeling fluid‐structure interactions with both strong and weak coupling. The objective was to determine the parietal deformations induced by thermodynamic conditions and pressure drops in the relevant vessels. The simulations involved hyperelastic and large deflection models to simulate the behavior of the wall. They allow the calculation of the numerical displacements and comparison with experimental displacements measured by magnetic resonance imaging, the aim is that the difference between numerical and experimental be as low as possible to deduce the adequate mechanical parameters for the artery. To identify the mechanical properties of the vessels, the optimization technique proposed in ANSYS based on genetic algorithms or gradient algorithms was used. One of the crucial points of identification involves the determination of the non‐stress state. If it is a known parameter for the elastic tube, it has to be determining for blood vessels. The challenge of this work is to determine from a “minimum” quantity of pressure and deformation information, the hyper‐elastic properties of blood vessels. The method based on a patient‐specific geometry deformation concluded that the tangent modulus in diastole is approximately 200 kPa while that in systole is in a range of 300 kPa to 1 MPa.