Molecular dynamics simulations were performed in an attempt to elucidate the molecular mechanism of a relaxation measured experimentally in poly(p-phenylene benzobisthiazole) (PBZT) fibres. Results for the coefficient of thermal expansion and tensile modulus parallel to the molecular axis agreed favourably with published experimental values. The X-ray peak intensity ratio of (200)/(010) versus temperature obtained from the simulations showed a variation qualitatively similar to that from experiments. The torsion angle between the benzobisthiazole and phenyl moieties increased with temperature. A distortion of the phenyl and benzobisthiazole moieties also occurred and the molecules were observed to undergo increased oscillatory ribbon-like motions perpendicular to the (010) plane as the temperature increased. Finally, translational oscillations of the molecules parallel to the c-axis occurred. These molecular motions are coupled to the tensile stress and could play a role in the relaxation.