High mechanical stress condition over the fibrous cap (FC) has been widely accepted as a contributor to plaque rupture. The relationships between the stress, lumen curvature, and FC thickness have not been explored in detail. In this study, we investigate lumen irregularity-dependent relationships between mechanical stress conditions, local FC thickness , and lumen curvature . Magnetic resonance imaging slices of carotid plaque from 100 patients with delineated atherosclerotic components were used. Two-dimensional structure-only finite element simulations were performed for the mechanical analysis, and maximum principal stress (stress-) at all integral nodes along the lumen was obtained. and were computed using the segmented contour. The lumen irregularity was defined as the difference between the largest and the smallest lumen curvature. The results indicated that the relationship between stress-, , and is largely dependent on . When (irregular lumen), stress- strongly correlated with lumen curvature and had a weak/no correlation with local FC thickness, and in 73.4% of magnetic resonance (MR) slices, the critical stress (maximum of stress- over the diseased region) was found at the site where the lumen curvature was large. When (relatively round lumen), stress- showed a strong correlation with local FC thickness but weak/no correlation with lumen curvature, and in 71.7% of MR slices, the critical stress was located at the site of minimum FC thickness. Using lumen irregularity as a method of identifying vulnerable plaque sites by referring to the lumen shape is a novel and simple method, which can be used for mechanics-based plaque vulnerability assessment.