This paper presents an introduction to the use of finite element methods in the simulation and analysis of intracranial blood flow and lays the foundation for more detailed clinically oriented studies. An overview of finite element theory is provided and includes the formulation of both the continuous and discrete equations of viscous fluid flow. A discussion of appropriate assumptions and boundary conditions governing arterial blood flow is presented. Two-dimensional, rigid-walled models are developed for flow in a straight artery, a 90 degrees curved artery and a bifurcated artery. For each model, a description of the finite element mesh, numerical solution and computational results are presented. This paper is the first in a series which will detail computational analysis of the relationship between pressure, velocity development of intracranial aneurysms and therapeutic approaches to aneurysm management. The goals of this research are to investigate the fluid dynamics that arise as a result of pulsatile flow in the arteries of the circle of Willis, relate these hemodynamics to the formation of aneurysms, develop a computational understanding of the effects of various therapies on blood flow related to aneurysms, and to develop and utilize patient specific computer simulations for treatment planning.