In this study, using fluid-structure interaction (FSI), 3-dimensional blood flow in an aneurysm in the circle of Willis – which is located in the middle cerebral artery (MCA) – has been simulated. The purpose of this study is to evaluate the effect of a partly blocked vessel on an aneurysm. To achieve this purpose, two cases have been investigated using the FSI method: in the first case, an ideal geometry of aneurysm in the MCA has been simulated; in the second case, modeling is performed for an ideal geometry of the aneurysm in the MCA with a partly blocked vessel. All boundary conditions, properties and modeling methods were considered the same for both cases. The only difference between the two cases was that part of the MCA parent artery was blocked in the second case. In order to consider the hyperelastic property of the wall and the non-Newtonian properties of the blood, the Mooney-Rivlin model and the Carreau model have been used, respectively. In the second case, the Von Mises stress in the peak systole is 26% higher than in the first case. With regard to the high amount of Von Mises stress, the risk of rupture of the aneurysm is higher in this case. In the second case, the maximum wall shear stress (WSS) is 12% higher than in the first case. And maximum displacement in the second case is also higher than in the first. So, the risk of growth of the aneurysm is higher in cases with a partly blocked vessel.