Based on the Asymptotic Homogenization Method, the electromechanical global behavior of a two-phase piezoelectric unidirectional periodic fibrous composite is investigated. The composite is made of homogeneous and linear transversely isotropic piezoelectric materials that belong to the symmetry crystal class 622. The cross-sections of the fibers are circular and are centered in a periodic array of rectangular cells. The composite state is anti-plane shear piezoelectric. Local problems that arise from the two-scale analysis using the Asymptotic Homogenization Method are solved by means of a complex variable, leading to an infinite system of algebraic linear equations. This infinite system is solved here using different truncation orders, allowing a numerical study of the effective properties. Some numerical examples are shown
