The majority of condensed polycyclic benzenoid aromatic hydrocarbons exist as highly nonplanar molecular structures. Group additivity methods, AM1 calculations, and molecular mechanics are compared as general tools for estimating relative and absolute stabilities in nonplanar members of this class of compounds and for correlating the sparse experimental DELTA-H(f)-degrees data. The AM1 computations give large, variable (positive) errors compared to the experimental DELTA-H(f)-degrees's, whereas molecular mechanics and group additivity precisely model the same data. Molecular mechanics calculations for 153 polybenzenoid compounds with up to seven benzenoid rings indicate that 72 are highly nonplanar. The ability of group additivity methods to represent structural strain and the energetic consequences of nonplanarity in the polycyclic benzenoids is demonstrated by a precise partition of the calculated molecular mechanics DELTA-H(f)-degrees as a sum of CC and CH bond energy terms, steric interference parameters, and resonance energies.