The inter-particle behavior that occurs within electrorheological (ER) materials was investigated numerically. In this initial phase of the study, a two-dimensional material assumption was adopted, and static situations were investigated. A unit cell geometry consisting of two particles separated by a fluidic carrier medium was selected, and hybrid cylindrical-numerically generated grid systems were utilized. With appropriate boundary conditions applied, electric potential distributions throughout unit cells were determined. Electric field and current distributions and resultant mechanical stresses were then calculated. Results are presented in the form of electric potential, field, and current distributions, as well as net inter-particle forces.