The electrostatic (or, in a better word, quasi-electrostatic) theory of waves propagation in a long, rectangular waveguide having perfect electric conductor walls that filled with an anisotropic medium (here, a medium of nanowire-based hyperbolic metamaterials) is presented. Some data on characteristics of these waves are prepared. The presented results include electrostatic field configurations (modes) that can be supported by such structures and their corresponding cutoff frequencies, group velocities, power flows and storage energies.
