Abstract: The family of Sombor indices(Sombor index, reduced Sombor index, modified Sombor index, etc.) show satisfactory predictive and discriminative potential in modeling entropy and enthalpy of vaporization of alkanes. The results of testing the predictive potential of the family of Sombor indices indicate that these descriptors may be successfully applied to modeling thermodynamic properties of compounds and have important value for chemical application. The expected values of the modified Sombor indices of four kinds of common polycyclic aromatic compounds—(random) hexagonal chains, (random) polyphenyl chains, (random) phenylene chains and (random) spiro chains are studied with recursive calculation. Furthermore, the extremal values and extremal graphs of the modified Sombor indices for these four kinds of polycyclic aromatic compounds are characterized respectively.