AbstractWe present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM). The SSTFSI technique includes the enhancements introduced recently by the T★AFSM to increase the scope, accuracy, robustness and efficiency of this class of techniques. The SSTFSI technique is supplemented with a number of special techniques developed for arterial fluid mechanics modeling. These include a recipe for pre‐FSI computations that improve the convergence of the FSI computations, using an estimated zero‐pressure arterial geometry, and the sequentially coupled arterial FSI (SCAFSI) technique. The recipe for pre‐FSI computations is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is also based on that assumption. The need for an estimated zero‐pressure arterial geometry is based on recognizing that the patient‐specific image‐based geometries correspond to time‐averaged blood pressure values. In our arterial fluid mechanics modeling the arterial walls can be represented with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element is made of hyperelastic (Fung) material. Test computations are presented for cerebral and abdominal aortic aneurysms, where the arterial geometries used in the computations are close approximations to the patient‐specific image‐based data. Copyright © 2007 John Wiley & Sons, Ltd.