Numerical simulations for the blood flow are carried out to investigate the effect of the flexible artery wall on the flow field and to determine the wall shear stresses in the carotid artery wall. To solve the equation of motion for the structure in typical fluid-structure interaction (FSI) problems, it is necessary to calculate the fluid force on the surface of the structure explicitly. To avoid complexity due to the necessity of additional mechanical constraints, we use the combined formulation including both the fluid and structure equations of motion into a single coupled variational equation. The Navier-Stokes equations for fluid flow are solved using a P2P1 Galerkin finite element method (FEM) and mesh movement is achieved using arbitrary Lagrangian-Eulerian (ALE) formulation. The Newmark method is employed to solve the dynamic equilibrium equations for linear elastic solid mechanics. The time-dependent, three-dimensional, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed. The study shows strongly skewed axial velocity and flow separation in the internal carotid artery (ICA). Flow separation results in locally low wall shear stress. Further, strong secondary motion in the ICA is observed.