We propose a technique to build artificial anisotropic dielectrics by using periodic insertions of a homogeneous material in a homogeneous substrate, characterized by a different dielectric constant. We calculate the effective dielectric constants corresponding to the three principal directions by means of dispersion diagrams associated to the periodic structure. The proposed method to realize low loss materials with controlled anisotropy has an important potential for applications, including nanomaterials and can be extended to the terahertz band by proper manufacturing technology.