Various Finite Element modeling concepts and linear analyses of 3D regular cellular solids (lattice structures) with relative densities ranging from 10% to 20% are presented. Continuum element based models and beam element based models are employed, the latter with and without an adaptation of stiffness in the vicinity of the vertices. Space filling unit cell models are used for a constitutive characterization of four different structures in terms of density and directional dependence of their Young's moduli. Finite structure models of different size are simulated for investigating the influence of free surfaces and being compared to results of uniaxial compression tests of samples fabricated by two different Rapid Prototyping techniques. (c) 2005 Springer Science + Business Media, Inc.