We demonstrate, by theoretical analysis and molecular dynamics simulation, a mechanism for fabricating nanotubes by self-bending of nanofilms under intrinsic surface-stress imbalance due to surface reconstruction. A freestanding Si nanofilm may spontaneously bend itself into a nanotube without external stress load, and a bilayer SiGe nanofilm may bend into a nanotube with Ge as the inner layer, opposite of the normal bending configuration defined by misfit strain. Such rolled-up nanotubes can accommodate a high level of strain, even beyond the magnitude of lattice mismatch, greatly modifying the tube electronic and optoelectronic properties.