Cardiovascular diseases including atherosclerosis and aneurysm are the leading cause of human mortality in the western world. The interrelation of the onset and development of such diseases with mechanical forces acting on and within the arterial wall represents a research field of eminent interest. The arterial wall is characterized by large deformations and strains as well as material inhomogeneity, anisotropy, viscoelasticity, and continuous remodeling. Its structural behavior is therefore highly non-linear. This dissertation is concerned with an advanced finite-element approach to model the arterial wall in structural simulations of patient-specific vessel geometries. With the help of a number of efficient numerical methods a modeling approach is developed which is well suited especially for patient-specific problems. Examples of real geometries of the aortic arch and the iliac bifurcations demonstrate the effectiveness of this approach.