The use of hydrocracked and straight-run vacuum residues in the production of road pavement bitumen requires a good understanding of how the viscosity and softening point can be modeled and controlled. Scientific reports on modeling of these rheological properties for hydrocracked and straight-run vacuum residues are scarce. For that reason, 30 straight-run vacuum residues and 33 hydrocracked vacuum residues obtained in a conversion range of 55–93% were investigated, and the characterization data were employed for modeling purposes. An intercriteria analysis was applied to investigate the statistically meaningful relations between the studied vacuum residue properties. It revealed that the straight-run and hydrocracked vacuum residues were completely different, and therefore their viscosity and softening point should be separately modeled. Through the use of nonlinear regression by applying CAS Maple and NLPSolve with the modified Newton iterative method and the vacuum residue bulk properties the viscosity and softening point were modeled. It was found that the straight-run vacuum residue viscosity was best modeled from the molecular weight and specific gravity, whereas the softening point was found to be best modeled from the molecular weight and C7-asphaltene content. The hydrocracked vacuum residue viscosity and softening point were modeled from a single property: the Conradson carbon content. The vacuum residue viscosity models developed in this work were found to allow prediction of the asphaltene content from the molecular weight and specific gravity with an average absolute relative error of 20.9%, which was lower of that of the model of Samie and Mortaheb (Fuel. 2021, 305, 121609)—32.6%.