In this paper we develop a computational approach to analyze hemodynamics in the aorta; this may serve as a useful tool in the development of noninvasive methods to detect early onset of diseases such as aneurysms and stenosis in major blood vessels. We introduce a mathematical model which describes the interaction of blood flow with the aortic wall; this model is based on the immersed boundary method. A two-dimensional vessel model is constructed, the velocity at the inlet is prescribed based on the information from the Magnetic Resonance Imaging data measured in the aorta of a healthy subject, and the velocity at the outlet is prescribed by driving the pressure level reproduced from the literature. The mathematical model is validated by comparing with well-known solutions of the viscous incompressible Navier-Stokes equations, i.e., Womersley flow. The hysteresis behavior in the pressure-diameter relation is observed when the viscoelastic material property of the arterial wall is taken into consideration. Five different shapes of aortic wall are considered for comparison of the flow patterns inside the aorta: one for the normal aorta, two for the dilated aorta, and two for the constrictive aorta.