High mechanical stress in atherosclerotic plaques at vulnerable sites, called critical stress, contributes to plaque rupture. The site of minimum fibrous cap (FC) thickness (FC(MIN)) and plaque shoulder are well-documented vulnerable sites. The inherent weakness of the FC material at the thinnest point increases the stress, making it vulnerable, and it is the big curvature of the lumen contour over FC which may result in increased plaque stress. We aimed to assess critical stresses at FC(MIN) and the maximum lumen curvature over FC (LC(MAX)) and quantify the difference to see which vulnerable site had the highest critical stress and was, therefore, at highest risk of rupture. One hundred patients underwent high resolution carotid magnetic resonance (MR) imaging. We used 352 MR slices with delineated atherosclerotic components for the simulation study. Stresses at all the integral nodes along the lumen surface were calculated using the finite-element method. FC(MIN) and LC(MAX) were identified, and critical stresses at these sites were assessed and compared. Critical stress at FC(MIN) was significantly lower than that at LC(MAX) (median: 121.55 kPa; inter quartile range (IQR) = [60.70-180.32] kPa vs. 150.80 kPa; IQR = [91.39-235.75] kPa, p < 0.0001). If critical stress at FC(MIN) was only used, then the stress condition of 238 of 352 MR slices would be underestimated, while if the critical stress at LC(MAX) only was used, then 112 out of 352 would be underestimated. Stress analysis at FC(MIN) and LC(MAX) should be used for a refined mechanical risk assessment of atherosclerotic plaques, since material failure at either site may result in rupture.