Intracranial aneurysms are anomalies near the bifurcations and curvatures in the cerebral circulatory system. The rupture of an aneurysm is a medical emergency with higher mortality rates. Understanding the disease initiation, progression, and rupture stages of an aneurysm is of clinical significance and valuable for patient management. However, this is greatly influenced by hemodynamic parameters, which can be obtained by computational fluid flow simulations. In the present study, the coupling between the fluid and arterial wall is resolved by accounting for the compliant nature of the walls by solving for both the flow field and structural dynamics. Patient-specific simulations are performed for a middle cerebral artery bifurcating aneurysm with three different elastic moduli (1 MPa, 2 MPa, and 3 MPa). FSI simulations reveal that an increase in elastic moduli results in reduced wall stresses and wall displacements with an attendant increase in fluid stresses. Rigid wall CFD simulations were found to overestimate the WSS values compared to FSI studies.