Metal rubber (MR) material is a new-type of damping material. Its raw material and fabrication process have same unique features. Wire helix is considered as the unit cell geometry of MR. Combining cylindrical compression coil spring theory, a mechanical model is established for individual wire helix which is located in the horizontal or longitudinal direction. Three contact statuses are analyzed for the neighboring helixes and mechanical models are derived for these cases according to the Kulun model. The arrangement and the spatial distribution of the microelements are assumed to be located evenly and periodically inside the MR. A mathematic model is established to characterize the damping behavior of MR. It came from the unit cell geometry and the fabrication process of MR materials. It is easy to explain the mechanism of hysteresis loop and the nonlinear stiffness and damping characteristic of MR by analyzing contact states and contact number of unit cell wire helixes. Finally, a comparison is made between theoretical results and experimental results. This model is valuable for the analysis of the material mechanics and the design of MR. It provides theoretical support for the further engineering application of MR in the field of vibration reduction.