The Eshelby method and the Fourier series are used in order to determine the linear elastic and viscoelastic properties of composites with periodically distributed inclusions in a non-orthogonal coordinate system. The relaxation moduli provided by the proposed method are compared with the moduli obtained via FEM for a unidirectional composite. This comparison gives good results. The procedure results very useful for periodic composites with hexagonal symmetry, such as some transversely isotropic composites.