A mathematical modeling for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed. The blood pressure acting on the inner arterial wall is modeled using a Fourier Series, the arterial wall is modeled using a spring-mass system, and the surrounding cerebral spinal fluid is modeled via a simplified Navier-Stokes equation. The resulting coupled system of partial differential equations for this fluid structure interaction with appropriate boundary conditions are solved first analytically using Laplace Transform and then numerically using an implicit finite difference scheme. The solutions are also investigated using computational tools. An application of the model studied to intracranial saccular aneurysms is also presented.