Fullerenes are closed cage carbon nanostructures and form the layers of carbon onions which have potential application in electronics industries. In this paper mechanical properties of such fullerenes are investigated using continuum shell models and Monte Carlo (MC) simulations. It is shown that elastic shell parameters originally derived for graphene or carbon nanotubes are also appropriate to model the shell properties of fullerene layers. A good representation of the MC results is obtained for effective elastic moduli of E ～ 5000 GPa in combination with an effective layer thickness of h ～ 0.07 nm. The most frequently proposed parameter set for carbon nanotubes with h ～ 0.34 nm and E ～ 1 TPa completely fails to predict the mechanical behavior of fullerenes. Further it is shown that the pentagonal atomic rings, required to form a closed cage structure, locally increase the hydrostatic stiffness of the faceted fullerenes, but also significantly reduce the stiffness of the surrounding hexagonal atomic rings. As the number of pentagons in a fullerene is restricted to 12 the proportion of the surface area covered by hexagons increases for larger fullerenes leading to a decrease in hydrostatic stiffness with fullerene size.
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