A head positioning instrument is provided for accurately modeling the position of a patients jaw for orthodontic, prosthodontic, dental, or orthognatic surgery treatment planning The horizontal distance between a pair of reference points that are visible on an x-ray are measured. These reference points are then utilized to ensure that substantially true vertical and substantially true horizontal are reflected in a radiograph. The patients lower jaw hinge is accurately located, and the upper jaw is located using a bite fork attached to the lower jaw hinge axis locator. The bite fork assembly contained within the lower jaw hinge axis locator is removed from the head positioning instrument and transferred to an axis mounting stand for accurate reproduction of the spatial positioning of the patients upper jaw. The patients individual characteristics are accurately preserved throughout the transfer and modeling process, resulting in accurate correspondence between the model and radiograph.