This study was undertaken to determine the geometric form of the surface on which a fixed point on the head moves as a result of neck motion. Motion of a retroreflective marker on the glabella of six normal subjects was stereoscopically recorded by two video cameras, during a variety of neck motions, performed on command. Near real-time computer analysis in three dimensions of the video images showed the marker moved on a surface that very closely approximated an elliptical paraboloid (with tendency to a hemisphere), after extraneous shoulder motion had been eliminated. Parameters defining the elliptical paraboloids were obtained. Using a reflex microscope, the shape of the articular facets on skull base and superior facets of C1 and C2 of 6 normal subjects were examined. The shapes of all these facets were calculated and also found to be elliptical paraboloids.