Abstract: Based on the elasto-perfectly plastic constitutive relation, two damping force models of lead shear dampers are deduced. Considering the assumption of the shear deformation equality and the simultaneous yield of the shear stress in the cross section, the equal deformation damping force model (equal model)is derived from the energy principle. One shear strain distribution function is introduced to describe the relation between the shear strain associated with the shear yield and the yield extent in the cross section based on the shear stress distribution and the deformation continuity. From the shear force balance equation in the cross section, the unequal deformation damping force model (unequal model)is formulated. Comparing two theoretical hysteretic loops with the experimental data obtained from Robinson Seismic Ltd, results indicate that the unequal model can accurately predict the experimental curves in both small and large displacements, while the equal model can approximately coincide with the experimental data in big displacements only. Consequently, the limit damping force of the unequal model proves the peak damping force (yield shear force)of the equal model. A proposed method is presented to design lead shear dampers according to the limit damping forces and yield displacements.