Dispersion and electrostatic interactions both contribute significantly to the tight assembly of macromolecular chains within crystalline polysaccharides. Using dispersion-corrected density functional theory (DFT) calculation, we estimated the elastic tensor of the four crystalline cellulose allomorphs whose crystal structures that are hitherto available, namely, cellulose Ia, Ib, II, III I . Comparison between calculations with and without dispersion correction allows quantification of the exact contribution of dispersion to stiffness at molecular level.