Viscoelastic damper is a kind of viscous damping device with stiffness. There are three types of load deformation hysteretic curves: linear, deformation softening and deformation hardening. Its mechanical model includes the model of applying fractional differential constitutive relation and the model of combining spring and damper. Its damping force is related to velocity and displacement. The shape of the damper includes plane type and barrel type. The viscoelastic damper is composed of viscoelastic damping material and constrained steel plate alternately laminated and bonded. In addition to the viscoelastic damping material, there are also constrained steel plate and adhesive layer. The latter two materials can hardly consume energy, so the loss factor of the viscoelastic damper is smaller than that of the viscoelastic material. The mechanical properties of viscoelastic dampers cannot be completely equal to the mechanical properties of viscoelastic damping materials. Under the action of external forces, the deformation of viscoelastic dampers is the sum of the deformation of viscoelastic damping materials, steel plates and adhesives.