We propose a theoretical model to show that pulling up an adatom from an atomic step requires a weaker force than from the flat surfaces of Al(0 0 1), Ni(1 1 1), Pt(1 1 0) and Au(1 1 0). Single adatom in the atomic step can be extracted vertically by a trimer-apex tip while can be released to the flat surface. This reversible vertical manipulation can then be used to fabricate a supported three-dimensional (3D) nanostructure on the Ni(1 1 1) surface. The present modeling can be used to predict whether the reversible vertical single-atom manipulation and thus the assembling of 3D nanostructures can be achieved on a metal surface. (C) 2012 Elsevier B.V. All rights reserved.