It is believed that atherosclerotic plaque rupture may be related to maximal stress conditions in the plaque. More careful examination of stress distributions in plaques reveals that it may be the local stress/strain behaviors at critical sites such as very thin plaque cap and locations with plaque cap weakness that are more closely related to plaque rupture risk. A "local maximal stress hypothesis" and a stress-based computational plaque vulnerability index (CPVI) are proposed to assess plaque vulnerability. A critical site selection (CSS) method is proposed to identify critical sites in the plaque and critical stress conditions which are be used to determine CPVI values. Our initial results based on 34 2D MRI slices from 14 human coronary plaque samples indicate that CPVI plaque assessment has an 85% agreement rate (91% if the square root of stress values is used) with assessment given by histopathological analysis. Large-scale and long-term patient studies are needed to further validate our findings for more accurate quantitative plaque vulnerability assessment.