Twenty-two straight run vacuum residues extracted from extra light, light, medium, heavy, and extra heavy crude oils and nine different hydrocracked vacuum residues were characterized for their bulk properties and SARA composition using four and eight fractions (SAR-ADTM) methods. Intercriteria analysis was employed to determine the statistically meaningful relations between the SARA composition data and the bulk properties. The determined strong relations were modeled using the computer algebra system Maple and NLPSolve with the Modified Newton Iterative Method. It was found that the SAR-ADTM saturates, and the sum of the contents of saturates and ARO-1 can be predicted from vacuum residue density, while the SAR-ADTM asphaltene fraction content, and the sum of asphaltenes, and resins contents correlate with the softening point of the straight run vacuum residues. The softening point of hydrocracked vacuum residues was found to strongly negatively correlates with SAR-ADTM Aro-1 fraction, and strongly positively correlates with SAR-ADTM Aro-3 fraction. While in the straight run vacuum residues, the softening point is controlled by the content of SAR-ADTM asphaltene fraction in the H-Oil hydrocracked vacuum residues, the softening point is controlled by the content of SAR-ADTM Aro-3 fraction content. During high severity H-Oil operation, resulting in higher conversion, hydrocracked vacuum residue with higher SAR-ADTM Aro-3 fraction content is obtained, which makes it harder and more brittle.