Carotid plaque surface irregularity and ulcerations play an important role in the risk of ischemic stroke. Ulcerated or fissured plaque, characterized by irregular surface morphology, exposes thrombogenic materials to the bloodstream, possibly leading to life- or brain-threatening thrombosis and embolization. Therefore, the quantification of plaque surface irregularity is important to identify high-risk plaques that would likely lead to vascular events. Although a number of studies have characterized plaque surface irregularity using subjective classification schemes with two or more categories, only a few have quantified surface irregularity using an objective and continuous quantity, such as Gaussian or mean curvature. In this work, our goal was to use both Gaussian and mean curvatures for identifying ulcers from 3D carotid ultrasound (US) images of human subjects. Before performing experiments using patient data, we verified the numerical accuracy of the surface curvature computation method using discrete spheres and tori with different sampling intervals. We also showed that three ulcers of the vascular phantom with 2 mm, 3 mm and 4 mm diameters were associated with high Gaussian and mean curvatures, and thus, were easily detected. Finally, we demonstrated the application of the proposed method for detecting ulcers on luminal surfaces, which were segmented from the 3D US images acquired for two human subjects.