The deformation of a foamed elastic material, both in tension and compression, and its resistance to tearing and to tensile rupture, have recently been derived on the basis of a model consisting of a large number of thin threads joined at their ends to form a three-dimensional network. A general account of this theoretical treatment, and the evidence for it, is presented. The theory is extended to deal with small deformations of closed-cell foams; relations for Young's modulus and Poisson's ratio are derived. The viscous damping of open-cell foams due to air flow through the network of threads is also discussed.