We have performed atomistic simulations on solid and hollow copper nanowires to quantify the elastic properties of hollow nanowires (nanoboxes). We analyse variations in the modulus, yield stress and strain for 100 and 110 nanoboxes by varying the amount of bulk material that is removed to create the nanoboxes. We find that, while 100 nanoboxes show no improvement in elastic properties as compared to solid 100 nanowires, 110 nanoboxes can show enhanced elastic properties as compared to solid 110 nanowires. The simulations reveal that the elastic properties of the nanoboxes are strongly dependent on the relative strength of the bulk material that has been removed, as well as the total surface area of the nanoboxes, and indicate the potential of ultralight, high-strength nanomaterials such as nanoboxes.