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 Iα, Iβ, II, IIII. Comparison between calculations with and without dispersion correction allows quantification of the exact contribution of dispersion to stiffness at molecular level.