Quantifying the changing shape of the tongue has been a longstanding challenge for experimental phonetics. One approach is to track the location of points on the tongue using x-ray microbeam or EMA. This leads to a precise numerical quantification, but is limited to information from a few points. Cinefluorography, MRI, and ultrasound remove the limitation by imaging entire sections of the tongue, but it is difficult to derive quantitative information from the scans. The present work illustrates a new method for quantifying an ultrasound tongue image by automatically fitting a conic arc to the midsagittal edge of the tongue. These arcs can vary continuously in shape from elliptic to parabolic to hyperbolic, and the variation is parametrized by two phonetically meaningful geometric parameters: one correlates with constriction location and the other with constriction degree. Quantification of tongue shape change is then measured by tracking the change in these 2 unique descriptors. One arc is sufficient for most tongue shapes, but some require two. Also, the general conic arc is a better model of the tongue dorsum than the circle, which has been used in articulatory synthesis systems. We will present data comparing these two models. [Work supported by NIH Grant DC-02717.]