A theoretical study of single-chain moduli employing the molecular-orbital semi-empirical AM1 (Austin model 1) approach is presented for the poly( p-phenylene benzobisimidazole) (PBI), poly( p-phenylene benzobisoxazole) (PBO) and poly( p-phenylene benzobisthiazole) (PBZT) rigid-rod polymers. This computational study is important for comparisons of mechanical properties for the series of related polymers. An analysis of molecular deformation on tension and compression of these rigid-rod polymers offers an insight into tensile and compressive processes at the molecular level, allowing their relative ordering by theoretical tensile and/or compressive strength and moduli. Furthermore, an examination of the electronic structures of these molecular systems containing various hetero atoms provides insight into the charge distribution and bond order changes on the application of strain. This approach will be useful for the relative prediction of the properties of polymers that have not yet been synthesized.