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The Rayleigh identity, based on a multipole expansion theory, is extended to analyse the forces between particlesin an electrorheological system. The shear modulus for chains of particles arrayed on a square lattice is calculated. Itis found that the modulus increases linearly with the ratio of dielectric constants of the dispersed particles to that ofthe continuous phase; as the ratio becomes larger, contrary to the expectations from a simple dipole approximation,the modulus would saturate. In the case of conducting particles, the modulus varies with the frequency of the appliedfield. In a limiting case of perfectly conducting particles, the conductivity is also considered. It is found that theparticle-particle forces are extremely sensitive to their separations from each other.