Abstract: An analytical method for the longitudinal shear problem of magnetoelectroelastic composites with double periodically distributed cylindrical fibers is presented by means of the Eshelb y’ s effective inclusion method, combining the theory of doubly periodic and quasi-periodic analytical functions. The solution in series is obtained. And explicit expressions for the stress, electric displacement and magnetic induction are derived.The influences of microstructure of such heterogeneous materials on its magnetoelectroelastic properties were discussed by the numerical examples. The present method provides an efficient tool for analyzing the magnetoelectroelastic properties and designing microstructure of composite materials.