Three-dimensional Voronoi models are developed to investigate the mechanical behavior of linearly elastic open cellfoams. Dependence of the Young_s modulus, Poisson_s ratio and bulk modulus of the foams on the relative density isevaluated through finite element analysis. Obtained results show that in the low density regime the Young_s modulusand bulk modulus of random Voronoi foams can be well represented by those of Kelvin foams, and are sensitive to thegeometric imperfections inherent in the microstructure of foams. In contrast, the compressive plateau stress of thefoams is less sensitive to the imperfections. Failure surface of the foams subject to multi-axial compression is determinedand is found to comply with the maximum compressive principal stress criterion, consistent with available experimentalobservations on polymer foams. Numerical results also show that elastic buckling of cell edges at microscopiclevel is the dominant mechanism responsible for the compressive failure of elastic open cell foams.