Copper sub-micron films are structured as columnar arrays of grains and are virtual two-dimensional polycrystalline solids. By modelling their plastic deformation by a two-dimensional flow of sliding deformable grains, a new perspective of the mechanical tests of Gruber et al. [Acta Mater. 56 (2008) 2318] is attained that reveals remarkable regularities which are missed by the more conventional analysis of the authors. The model shows that two-dimensional plasticity has significant qualitative differences from the three-dimensional counterpart. (c) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.