This report addresses two problems in the study of the shape of human dental arches; (1) the description of arch shape by mathematical functions and (2) the description of variation among the dental arch shapes in a population. A new algorithm for fitting conic sections is used to model the maxillary dental arches of a sample of sixty-six subjects. A statistical model for shapes represented by arcs of conic sections is demonstrated on the sample of sixty-six dental arches. It permits the definition of an "average shape" and the graphic representation of variation in shape. The model and methods of analysis presented should help dental scientists to better define and quantify "normal" or "ideal" shapes and "normal ranges of variation" for the shape of the dental arch.