Electrorheological- (ER-) fluid-based dashpot dampers have smart capabilities because ER fluids undergo large changes in yield stress as electric field is applied. Our objective is the development and experimental validation of quasi-steady dashpot damper models, based on an idealized nonlinear Bingham plastic shear flow mechanism, for purposes of preliminary design and performance predictions. The data required for the Bingham plastic model is normally supplied by ER fluid suppliers, that is, plastic viscosity and dynamic yield stress as a function of applied field, as determined from a shear stress versus shear strain rate diagram. As force is applied to the dashpot damper, the ER fluid flows through an annulus between the concentric inner and outer electrodes. The idealized Bingham plastic shear flow mechanism predicts that three annular flow regions develop as a function of the local shear stress. In the central pre-yield or plug region, the local shear stress is less than the dynamic yield stress, so that the plug behaves like a rigid solid. The remaining two annular regions, adjacent to the electrodes, are in the post-yield condition and correspond to the shear stress exceeding the dynamic yield stress, so that the material flows. Equivalent viscous damping performance of an ER fluid dashpot damper is strongly coupled with the plug behavior. For a constant force, as the applied field increases, so does the plug thickness and equivalent viscous damping. For a constant applied field, as the force increases, the plug thickness and equivalent viscous damping both decrease. The passive and active or field-dependent damping behavior of an ER-fluid-based dashpot damper can be designed for a specific application using these quasi-steady Bingham plastic models.