A foam is considered open-celled if at least two of its facets are holes rather than walls.  In this case the entirety of the load on the foam is on the cross-beams that make up the edges of the cell.  If no more than one of the walls of the cell are holes, the foam is considered closed-celled in nature.  For most synthetic foams, a mixture of closed cell and open cell character is observed due to cells rupturing during the foaming process and then the matrix solidifying.
The mechanical properties of the foam then depend on the closed cell character of the foam as derived by Gibson and Ashby:
Where E is the elastic modulus, ρ is the density of the material, φ is the ratio of the volume of the face to the volume of the edge of the material, and the subscript s denotes the bulk property of the material rather than that of the foam sample.