Steady flow of an ER (electro-rheological) fluid in a two-dimensional electrode channel is studied by using FEM. Hydrodynamic interactions between the particles and the fluid are calculated by solving the Navier-Stokes equation combined with the equation of motion for each particle, where the multi-body electrostatic interaction is described by using point-dipole model. Motion of the particles in the ER fluid is elucidated in conjunction with the mechanisms of the flow resistance and the increase of viscosity. The ER effects have been studied by varying the Mason number and volume fraction of particles. These parameters have an influence on the formation of the chains resulting in the changes of the fluid velocity and the effective viscosity of ER fluids.