The elastic tensors of chitin and chitosan allomorphs were calculated using density functional theory (DFT) with and without the dispersion correction and compared with experimental values. The longitudinal Young's moduli were 114.9 or 126.9 GPa for alpha-chitin depending on the hydrogen bond pattern: 129.0 GPa for beta-chitin and 191.5 GPa for chitosan. Furthermore, the moduli were found to vary between 17.0 and 52.8 GPa in the transverse directions and between 2.2 and 15.2 GPa in shear. Switching off the dispersion correction led to a decrease in modulus by up to 63%, depending on the direction. The transverse Young's moduli of a-chitin strongly depended on the hydroxylmethyl group conformation coupled with the dispersion correction, suggesting a synergy between hydrogen bonding and dispersion interactions. The calculated longitudinal Young's moduli were, in general, higher than experimental values obtained in static conditions, and the Poisson's ratios were lower than experimental values obtained in static conditions.