We develop a chain model of an electrorheological fluid in steady and oscillatory shear. This model is based on a balance of hydrodynamic and electrostatic forces and focuses on the mechanical stability of chains. With this model we compute the shape and orientation of an unconfined dipolar chain in steady shear as a function of the shear rate and electric field, and show that this leads to the expected shear-thinning viscosity. We then demonstrate that chains confined by electrodes are unstable in some Mason number regimes. The chain model is extended to the case of oscillatory shear by including a kinetic equation for the aggregation and fragmentation of chains. The resultant chain dynamics is found to be strongly nonlinear, as is the theology. Finally, we consider the effect of local field corrections and long range interactions on the bare dipolar interaction force and derive a self-consistent pair interaction force that demonstrates that the maximum orientation of a chain in shear depends strongly on the dielectric contrast.