We demonstrate the concept of inducing stresses in thin films post-deposition (extrinsic stress) to curve nanostructures on demand. The remarkably high extrinsic stress, induced by triggering grain coalescence in Sn thin films, was used to self-assemble 3D nanostructures with radii of curvature as small as 20 nm. The fabrication methodology required only simple processing steps and the self-assembly process was highly parallel. Curved nanostructures with any desired pattern and both homogeneous (rings, tubes) and variable radii of curvature (spirals, talons) could be constructed.