The homogenization problem of linearly piezoelectric fibrous composites with a periodic microstructure is formulated by adopting the free- and complementary-energy minimum principles, as well as the hashin-shtrikman principles. The auxiliary electroelastic problems involved in the hashin-shtrikman principles are solved by a transformation from the space domain to the fourier domain. Approximations of those variational principles, suitable for numerical computations, are built up by adopting the fourier-series method and the finite-element method. In this way, rigorous upper and lower bounds on the overall material moduli are obtained. An example is presented, in order to show the effectiveness of the proposed approximation techniques and to compare them.