Reliable simulation of molecular adsorption onto cellulose surfaces is essential for the design of new cellulose nanocomposite materials. However, the applicability of classical force field methods to such systems remains relatively unexplored. In this study, we present the adsorption of glucose, cellobiose, and cellotetraose on model surfaces of crystalline cellulose Iα and Iβ. The adsorption of the two large carbohydrates was simulated with the GLYCAM06 force field. To validate this approach, quantum theoretical calculations for the adsorption of glucose were performed: Equilibrium geometries were studied with density functional theory (DFT) and dispersion-corrected DFT, whereas the adsorption energies were calculated with two standard density functional approximations and five dispersion-containing DFT approaches. We find that GLYCAM06 gives a good account of geometries and, in most cases, accurate adsorption energies when compared to dispersion-corrected DFT energies. Adsorption onto the (100) surface of cellulose Iα is, in general, stronger than onto the (100) surface of cellulose Iβ. Contrary to intuition, the adsorption energy is not directly correlated with the number of hydrogen bonds; rather, it is dominated by dispersion interactions. Especially for bigger adsorbates, a neglect of these interactions leads to a dramatic underestimation of adsorption energies.