This series of papers covers several aspects related to the influence of external stresses on the crystalline microstructure of rigid-rod polymer-based fibres. For the study, the main three fibres of this type have been selected, namely poly(p-phenylenebenzobisoxazole) (PBO fibres), poly(p-phenylenebenzobisthiazole) (PBT or PBZT fibres) and the novel poly{2,6-diimidazo[4,5-b:4'-5'-e]pyridinylene-1,4(2,5dihydroxy)phenylene} (PIPD or M5 fibres). Synchrotron radiation was employed to record high-quality wide-angle X-ray scattering patterns from single fibres. The present paper deals mainly with the evaluation of lattice strain along the fibre axis (c-)direction. Crystal moduli of the different fibres were calculated from the variation with stress of the lattice strain determined from the shift of the major meridional (00l) reflections. This procedure rendered values of approximately 440 GPa for the crystal modulus of PIPD and PBO fibres, and 350 GPa for the PBT one. The difference between these two values was explained in tenus of specific molecular conformation of the monomers in the unit cell. Discrepancies between the crystal and macroscopic (calculated from tensile tests) moduli are due to imperfections generated during the manufacture of the fibres.