The simulation of the physiological loading situation of arteries with moderate atherosclerotic plaque may provide additional indicators for medical doctors to estimate if the plaque is likely to rupture and if surgical intervention is required. In particular the transmural stresses are important in this context. They depend strongly on the mechanical response and thus, a predictive material model capturing all characteristics of the material behavior is required. Here, polyconvex strain energy functions are considered for the hyperelastic behavior and a simplified viscoelastic model is proposed which does not take into account an isochoric strain energy for the fiber response. Based thereon, a comparative study is presented, investigating the influence of viscoelasticity on the mechanical behavior of a simplified arterial wall and a rather small impact is found. Realistic predictions of transmural stress distributions require a simulation of the interaction between the blood flow and the vessel wall. We recall the equations that model fluid-structure interaction and the monolithic Convective Explicit algorithm for their numerical approximation, addressing both the cases when the fluid-structure meshes are conforming and nonconforming at the interface. We also present numerical experiments, using the monolithic approach, for the fluid structure interaction problem in a curved tube using a hyperelastic material model for the structure and an absorbing boundary condition. The fluid structure interaction using a highly nonlinear anisotropic structural model for the solid in this context is one of the main contributions of this paper.