Intracranial saccular aneurysms are balloon-like distensions of the arterial wall; they increase in size gradually, a few to the point of bleeding or catastrophic rupture. Collagen is the primary structural component of the aneurysmal wall, and because only a small fraction of aneurysms fail, the collagen fabric must effectively reorganize in order to maintain mechanical integrity as an aneurysm changes size. Data were obtained from four human aneurysms, fixed at 110 mmHG of distending pressure with 10% buffered formalin, and sectioned completely through at 4 microns thickness. Each set of measurements included groups of data taken layer by layer from a radial corridor across the aneurysm wall. Each three-dimensional orientation measurement, for which we used a Zeiss polarizing microscope with a universal stage attachment, is defined by an azimuth and elevation angle relative to the section plane. We compared the interdependence of these measured angles with a mathematical model based on fibres following great circle trajectories, and related the measured azimuth and elevation angles to the relative depth of the section into the aneurysm. Data were plotted on Lambert equal-area projections, along with the theoretical relation between azimuth and elevation, that included wall thickness and depth of sectioning. The graphical relationship between measured azimuth and elevation for collagen fibres across the layered fabric of the aneurysmal wall is consistent with the theoretical great circle trajectories for collagen fibre alignment. Analysis was based on statistics for spherical data to give values for the mean orientation and the circular standard deviations (CSD) about that mean. The results indicate that any given region on the aneurysm wall is made up of many, very thin sublayers, most of which have a relatively coherent organization (mean CSD 8 degrees). These measurements agree well with the mathematical model and, when considered collectively, the layers provide a balanced distribution for bearing the biaxial tensile stress of the wall.