The systems considered here are composed of noninteracting ideal chains, formed from many identical beads, each of which is bound to its two nearest neighbors with an arbitrary potential of interaction. The thermodynamic properties of these systems are examined for several bond potentials. Comparisons then are made between the properties of the model systems and the experimentally observed behaviors of rubbery materials. Connections also are established between the thermodynamic and elastic properties of these model systems and those given by the traditional theories of polymeric elasticity.