Hemodynamic factors such as the wall shear stress play an important role in the pathogenesis and treatment of cerebral aneurysms. In present study, we apply computational fluid-structure interaction analyses on cerebral aneurysms with two different constitutive relations for aneurismal wall in order to investigate the effect of the aneurismal wall mechanical properties on the simulation results. We carry out these analyses by using two patient-specific models of cerebral aneurysms of different sizes located in different branches of the circle of Willis. The models are constructed from 3D rotational angiography image data and blood flow dynamics is studied under physiologically representative waveform of inflow. From the patient models analyzed in this investigation, we find that the deformations of cerebral aneurysms are very small. But due to the nonlinear character of the Navier-Stokes equations, these small deformations could have significant influences on the flow characteristics. In addition, we find that the aneurismal-wall mechanical properties have great effects on the deformation distribution of the aneurysm, which also affects the wall shear stress distribution and flow patterns. Therefore, how to define a proper constitutive relation for aneurismal wall should be considered carefully in the hemodynamic simulation.