Based on traditional bilinear hysteresis model of elastomeric damper, slide hysteresis force can be equivalent to viscous damping force and piecewise linear elastic force for identifying parameters easily, and decaying exponential function is introduced to indicate the changing rule of elastic force and damping force with excitation amplitude. Complex modulus model is established for elastomeric damper with static shift, and a parameter identification method on the basis of complex modulus and hysteresis loop is presented. Then the accuracy of improved model and effectiveness of parameter identification method are all validated by numerical examples. The influence of static shift on hysteresis loop and complex modulus are analyzed. The results show that:hysteresis loop moves along the elastic force curve with static shift changing, and the form of hysteresis loop changes on account of nonlinear stiffness. When the model uses odd order elastic force and linear damping force, storage modulus appears even order function changing with static shift, and loss modulus is invariant. The influence of static shift on storage modulus and loss modulus is attributed to nonlinear stiffness and damping with displacement.