Nanopaper is a transparent film made of network-forming nanocellulose fibrils. These fibrils are several micrometers long with a diameter of 4–50\,nm. The reported elastic modulus of nanopaper often falls short of even conservative theoretical predictions based on the modulus of crystalline cellulose, although such predictions usually perform very well for macroscopic fiber materials, such as paper or fiber composites. We investigate this inconsistency and suggest explanations by identifying the critical factors affecting the stiffness of the nanopaper: The effect of drying constraints cannot solely explain the relatively low elastic modulus of nanopaper. Among the factors that showed the most influence is the presence of noncrystalline regions along the length of the nanofibrils, initial strains within the network structure and the three-dimensional structure of individual bonds.