  Most cellular solids are random materials, while practically all theoretical
results are for periodic models. To be able to generate theoretical results for
random models, the finite element method (FEM) was used to study the elastic
properties of solids with a closed-cell cellular structure. We have computed
the density ($\rho$) and microstructure dependence of the Young's modulus ($E$)
and Poisson's ratio (PR) for several different isotropic random models based on
Voronoi tessellations and level-cut Gaussian random fields. The effect of
partially open cells is also considered. The results, which are best described
by a power law $E\propto\rho^n$ ($1 < n <2$), show the influence of randomness
and isotropy on the properties of closed-cell cellular materials, and are found
to be in good agreement with experimental data.
