Based on the typical mesoscopic structural characteristics of metal rubber, the mesoscopic physical mechanism was revealed, through analyzing the spatial configuration and contact mode of wire helixes for its compression deformation process. The mesoscopic structure unit based on the curved beam of variable length and the model of contact interaction between curved beams were presented, and combined with the distribution law of frictional contact points, a new constitutive model of metal rubber for hysteresis characteristics was established, which included its basic structure parameters which were the diameter and elastic modulus of wire, the diameter of wire helix, the relative density of metal rubber and so on. The model could describe the restoring force curves of metal rubber in initial loading, unloading and repeated loading phases, and theoretically explained its elastic characteristics and dry friction damping characteristics of multipoint contact. To verify the theory model, a comparison was made between the theoretical results and the experimental results for metal rubber specimens with different relative densities. The results show that theoretic calculations are consistent with the experimental data. It provides a theoretical basis for predicting the stiffness and damping of metal rubber and guiding its design.