A rigorous method for the homogenization of general elastoplastic periodic lattices is applied to 3D cellular solids. Tetrakaidecahedral unit cell problems are solved to determine the overall yield surface of foams. Non-symmetric material distribution is introduced and new results concerning the influence of this type of defect are obtained. They show that non-uniform material distribution increases the overall strength, except in particular loading directions and that non-symmetry has no significant influence on the yield surface. (c) 2005 Springer Science + Business Media, Inc.