The plastic unit with a yielding process is used to describe rubber’s amplitude-related characteristic, and the method to identify the number of plastic unit and the distribution of the yielding point is researched. A novel hyperelastic-viscoelastic-plastoelastic constitutive model of rubber is built and its parameters are identified according to the results of the rubber material property experiments. The theoretical model is transfered into the material parameters of rubber in the finite element software, which are used to create the finite element model of rubber material. Finite element simulation results of rubber are in good agreement with the experimental results, so the model can be used for subsequent modeling of rubber bushing and analysis of suspension system.