Identifying the boundary of the optic cup excavation is of critical importance in the assessment of glaucomatous risk. Currently, most approaches are focused on the use of pallor. We present an automatic method to determine the cup excavation boundary based on vessel kinking in non-stereo retinal fundus images. The method tracks vessels using a self-initialized evolving model which adapts during propagation. A piecewise analysis of the vessel trajectory is conducted to determine vessel kinking locations, from which the optic cup is obtained. Our proposed method is validated on a large database of 618 images. The results suggest that our proposed method is able to obtain a more accurate cup excavation detection than other tested methods.