Rayleigh's formalism is generalized for the evaluation of the effective material properties in multicoated circular fibrous multiferroic composites. The derived solution is applied to the special three-phase composite in which coated fibers are embedded in a matrix. For composites made of piezoelectric (BaTiO 3) and piezomagnetic (CoFe 2 O 4 or Terfenol-D) phases, we find that the magnetoelectric effect in the composite made of CoFe 2 O 4 coated BaTiO 3 in matrix Terfenol-D is five times larger than that in the composite made of BaTiO 3 coated Terfenol-D in matrix CoFe 2 O 4. Furthermore, in each case, with appropriate coating to the circular fiber, the magnetoelectric effect in the coated composites can be enhanced by more than one order of magnitude as compared to the corresponding noncoating composite. V