Electrorheological (ER) material behavior exhibits a transition from viscoelastic properties in the pre-yield region to viscous properties in the post-yield region. A nonlinear dynamic model based on linear shear flow mechanisms is proposed to describe ER fluid behavior. The nonlinear model combines a 3-parameter fluid element and a viscous (dashpot) element using sigmoidal weighting functions. The weighting functions are dependent on the strain rate and serve to enforce the transition between the viscoelastic and the viscous characteristics. The model is then extended to characterize a damper based on ER fluids. A single-degree-of-freedom system incorporating an ER fluid damper is considered and its dynamics studied via numerical simulations. The results of the simulations show that, as the applied electric field is increased, a significant attenuation in the amplitude can be achieved, while the response changes significantly. A system identification methodology is suggested to determine the model parameters from simple vibration experiments. An important issue of the amplitude dependence of the material behavior is addressed and modifications to the model suggested so as to incorporate these effects.