A technique of embedding, sectioning and analysis has been developed for studying the orientation and proportional composition of smooth muscle in the straight portions of human major cerebral arteries. Various distortions, which occurred during processing and sectioning, were measured quantitatively. Nerve fibres were implanted as a reference frame within the paraffin block containing an arterial bifurcation. The nuclei of smooth muscle have been treated as three-dimensional vectors of cellular orientation. The projected length in the plane of the section and the section thickness were used to define section pitch. To relate these vectors to the overall geometry of cerebral arteries they were transformed such that the resultant pitch would be the same as that observed if the sections were cut normal to the arterial longitudinal axis. Matrix transformations of nuclear vectors were of the expansion and Eulerian forms. The average pitch for the five sections from three straight portions was -0.22 degrees +/- 2.36 (SD of five means) with a range between -2,8 degrees and 3.2 degrees. Because this pitch is small it is possible to use 6.9 micrometers thick longitudinal and mid-plane sections of straight arteries to obtain estimates of proportional composition. Stereological point counting was used to determine that smooth muscle comprised 72.0% +/- 4.76 (SD for ten segments) of the tunica media in cerebral arteries.