Nowadays, biomechanical methods are useful to identify the cause and treating of diseases. One of these diseases is the cerebral aneurysm. This disease starts by the inflation of artery wall and then by rupturing, it leads to intracranial hemorrhage. Therefore, it leads to morbidity or even it is the cause of the mortality for many patients. For this reasons, it is important to anticipate the emersion, growth and the rupture of a cerebral aneurysm. Computational fluid dynamics (CFD) and 2-way fluid-structure interaction (FSI) are common methods for interrogation the rupture of aneurysms and evaluating the effective hemodynamic parameters. In this study, they were employed to obtain appropriate information of a cerebral aneurysm. A patient-specific giant aneurysm was chosen in the internal carotid artery (ICA). Mooney-Rivlin parameters were used for the solid part and a non-Newtonian Carreu model was employed in the fluid part. Important hemodynamic parameters such as wall shear stress (WSS), time average wall shear stress (TAWSS), spatial average wall shear stress (SAWSS), oscillatory shear index (OSI), and relative residence time (RRT) were discussed. In addition, these methods were then compared and the number of cycles assessed to determine the accuracy of the solutions. Both methods illustrate a similar location for the risk of a rupture related to these hemodynamic parameters but with different quantities. The novelty of this works lies at the feasibility of using the FSI and CFD methods to show the cost function in the future clinical decision-making.