The work reports on the development of random three-dimensional Laguerre-Voronoi computational models for open cell foams. The proposed method can accurately generate foam models having randomly distributed parameter values. A three-dimensional model of ceramic foams having pre-selected cell volumes distribution with stochastic coordinates and orientations was created in the software package ANSYSTM. Different groups of finite element models were then generated using the developed foam modeling procedure. The size sensitivity study shows that each of foam specimens at least contains 125 LV-cells. The developed foam models were used to simulate the macroscopic elastic properties of open cell foams under uni-axial and bi-axial loading and were compared with the existing open cell foam models in the literature. In the high porosity regime, it is found that the elastic properties predicted by random Laguerre-Voronoi foam models are almost the same as those predicted by the perfect Kelvin foam models. In the low porosity regime the results of the present work deviate significantly from those of other models in the literature. The results presented here are generally in better agreement with experimental data than other models. Thus, the Laguerre-Voronoi foam models generated in this work are quite close to real foam topology and yields more accurate results than other open cell foam models.