Mechanism of dry-friction damping and nonlinear stiffness for metal ic rubber is a more complex problem. Lots of dry-fric-tion contact exist inside the material. Lots of vibration energy is dissipated by the friction and contact between spiral metal wires. The dry-friction damping is closely related to microstructure of object surface. In the paper, the mechanism of the dry-friction damp-ing for the metal ic rubber is analyzed from microcosmic point of view. In order to show vibration-reduced regularity of dry-friction damping, mathematics models, describing dry-friction regularity, must be put forward correctly. Because of non-smooth nonlinear constitutive relationship of the metal ic rubber, it is difficult to compute response of metal ic rubber structure with dry-friction seg-ment. In this paper, four mathematics models for dry-friction problem between two solid surfaces are introduced, that is, Sgn fric-tion model, hysteresis model, numerical calculation model of dry-friction inside dynamic system, three nonlinear viscous damped bilinear hysteretic model. The four mathematics models lay a solid foundation for further study of later generations in the field of me-tal ic rubber.%金属橡胶材料干摩擦阻尼、非线性刚度的产生机理是一个较为复杂的问题，其内部存在大量的干摩擦接触，通过螺旋型金属丝相互摩擦接触来损耗振动能量。干摩擦阻尼与物体表面的微观结构密切相关，从微观角度分析了金属橡胶材料干摩擦阻尼的产生机理，欲准确地揭示干摩擦阻尼的减振规律，还必须正确的提出描述干摩擦规律的数学模型。由于金属橡胶客观存在不光滑的非线性泛函本构关系，使得含有干摩擦环节的金属橡胶结构的响应计算问题非常困难。介绍了关于两固体接触表面间的干摩擦问题的四种数学模型，即Sgn摩擦模型、滞迟模型、动态系统中干摩擦力的数值计算模型、三次非线性粘性阻尼双线性滞迟模型，这四种模型为后人在该领域的继续研究奠定了坚实的理论基础。
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