The transition from two-dimensional (2D) to three-dimensional (3D) granular packings is studied using large-scale discrete element computer simulations. We focus on vertical stress profiles and examine how they change with dimensionality. We compare results for packings in 2D, quasi-2D packings between flat plates, and 3D packings. Analysis of these packings suggests that the Janssen theory does not fully describe these packings, especially at the top of the piles, where a hydrostaticlike region of vertical stress is visible in all cases. We find that the interior of the packing is far from incipient failure, while, in general, the forces at the walls are close to incipient failure. (C) 2004 Elsevier B.V. All rights reserved.