Mechanical properties of cellular solids depend on the ratio of the sample size to the cell size at length scales where the two are of the same order of magnitude. Considering that the cell size of many cellular solids used in engineering applications is between 1 and 10 mm, it is not uncommon to have components with dimensions of only a few cell sizes. Therefore, both for mechanical testing and for design, it is important to understand the link between the cellular morphology and size effects, which is the aim of this study. In order to represent random foams, two-dimensional (2D) Voronoi tessellations are used, and four representative boundary value problems - compression, shear, indentation, and bending - are solved by the finite element (FE) method. Effective elastic and plastic mechanical properties of Voronoi samples are calculated as a function of the sample size, and deformation mechanisms triggering the size effects are traced through strain maps. The modeling results are systematically compared with experimental results from the literature. As a rule, with decreasing sample size, the effective macroscopic stiffness and strength of Voronoi samples decrease under compression and bending, and increase under shear and indentation. The physical mechanisms responsible for these trends are identified. (C) 2010 Elsevier Ltd. All rights reserved.