The fundamental assumption of the paper is that the extra stress tensor tau of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation scs (n) over cap and length N of the fibers formed by application of an electric field). The resulting constitutive equation for tau is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate scs (gamma)over dot is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for (gamma)over dot --> infinity the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of (n) over cap and N on (gamma) over dot leads to the Bingham behavior for (gamma)over dot --> 0 and power law behavior for large shear rates.