Polymers are an important category of engineering materials, and are widely used in a variety of areas such as mechanical, construction, automotive, electrical appliances, light industry, electronics, and aerospace. Because of their unique molecular chain structures and aggregation structures, polymers have different physical properties compared with other materials, especially their mechanical properties. The mechanical properties of a polymer strongly depend on the conditions of temperature, loading time, deformation rate, and load frequency. Usually-depending on different temperatures and the time of observation-a polymer shows different mechanical behaviors including the glassy state, the viscoelastic state, the high-elastic state (hyperelastic or rubbery state), and the viscous flow state. As a structural material, the main features of a polymer's mechanical properties are its viscoelasticity and its hyperelasticity. This chapter will introduce viscoelasticity and its mechanical models, the hyperelasticity of polymer materials, and the yield and pattern of the brittle-ductile transition of polymer materials.