Arterial wall mechanics has been studied for nearly 200 years. This subject is of importance if we are to gain a fundamental understanding of this complex biological structure, as well as information needed to design prosthetics. Biomechanical arterial models continue to play an important role in the study of atherosclerosis, a disease of the arterial wall that is the chief cause of mortality and morbidity in the United States and the Western World. Over the past 20 years, the finite element model (FEM) has been used in a variety of ways to simulate the structural response of large arteries. Our purpose is to summarize the uses of FEMs in arterial mechanics. We will also indicate directions for future research in this area. A specialized FEM was described in the literature for the study of transport in the arterial wall, however the convection was not directly linked to arterial wall mechanics. In this paper special attention will be given to the development of FEMs based on the poroelastic view of arterial tissues which couple wall deformation, free tissue fluid motion, and associated transport phenomena in the arterial wall. In the future such models should provide fundamental quantitative information relating arterial wall mechanics and transport which may lead to a better understanding of both normal arterial physiology and atherogenesis.