Finite element methods are well-suited for solving problems in arterial fluid dynamics, primarily due to their ability to handle flows in complex geometries. However, in order to use these computational methods to develop realistic models of pulsatile flow in intracranial arteries and associated aneurysms, it is necessary to construct a 3-D mesh, or grid, that accurately duplicates the arterial geometry of interest. In this paper, we present an efficient method to accurately develop realistic 3-D computational meshes of human intracranial arteries and aneurysms from serial magnetic resonance angiography images. However, these techniques may be applied to any other form of imaging data including computed tomographic angiography. First, raw grayscale images are segmented, converted to their binary form and arterial contours are extracted at each image slice. Next, the arterial contours are stacked and cubic splines are computed along the axial direction. This creates an affect similar to smooth integration in the axial direction and provides a set of points that define the 3-D arterial surface geometry. Then, surface patches are constructed and merged. A surface mesh is then computed with the ability to locally vary the mesh density as desired. Finally, nodal points on the surface mesh are used to compute the finite element volume mesh. The 3-D volume mesh accurately describes the arterial geometry and is used to develop patient-specific computational fluid dynamic models of flow phenomena in intracranial arteries and aneurysms. These flow models are then suitable for investigating the hemodynamics of intracranial aneurysm formation and test the end-effects of various medical and surgical treatments.