The effective elastic moduli of a particle-filled material are analytically derived from a consideration of the deviations of the particle and matrix materials from either parallel or series connection. In the analysis an equivalent cell is defined based upon the operation of a force or deformation in an elementary cell representative of the composite; in addition, so-called particle and matrix stresses and strains are introduced. These parameters enable an expression for the respective energies of the constituents to be derived from both the parallel and series connection approach. The equation of both expressions gives the elastic modulus of the composite. This holds for six of the nine moduli. The other three are derived from separate considerations. The expressions obtained involve the way in which the particles are arranged, their shape and volume fraction, and the relevant elastic moduli of both materials. The numerical results are in good agreement with experimental values.