We analyze a simplified coupled model for aortic blood flow. The vessel wall reaction to the fluid is modeled by the Surface Pressure Model which assumes that the normal stress on the fluid is proportional to the displacement of the structure. This leads to a unique boundary problem for Navier-Stokes equations, where at the wall the velocity is normal to the wall, and proportional to the time derivative of the pressure. We prove that the problem is well posed and show that a semi-implicit time discretization converges. We present some numerical results and a comparison with a standard implementation of the Surface Pressure Model where the displacement is not eliminated.