The mechanical response of the solid state of a rigid rod polymer was evaluated through the static deformation of atomistic models. The calculations were applied to a set of polymorphs of poly(p-phenylene terephthalamide) (PPTA) previously deduced by molecular mechanics analysis. A series of simulated deformations of the minimum energy structures was used to predict all 21 independent elements each of the stiffness and compliance tensors. The significance of entropic and intermolecular potential contributions, in addition to the intramolecular potential contributions previously considered, to the accurate estimation of theoretical clastic moduli in such densely packed stiff chain polymer solids was elucidated. It was found that chain packing and entropy, or thermal motion, both have a significant effect on the fibre tensile modulus, but that they are of opposite sign and partially compensate. Elastic properties of aramid fibres were estimated by symmetrizing the single crystal elastic tensors in the limits of uniform strain and stress to yield Voigt and Reuss bounds, respectively, for the elastic moduli. For one structure of PPTA (closely resembling the crystallographically determined modification 1) the calculated extensional, transverse, and torsional moduli are in the ranges 220-290, 5.2-19 and 4.1-12 GPa, respectively, in good agreement with observed values.