Here we present the phase constant dependencies of propagating eigenmodes of open cylindrical anisotropic metamaterial waveguide when the metamaterial permittivity and permeability tensor components may accept values close or equal to zero. Dispersion characteristics of rod and hollow-core waveguides with the radii 0.5, 2.5 and 5 mm at the left handed polarization of microwave are shown here. There are unusual shape of eigenmode dispersion characteristics and anomalous sectors of the characteristics at certain frequencies. The first eigenmode of rod waveguide with the lowest cutoff frequency is a particularly important mode because it is a single one in the frequency range 1.0–1.9 GHz and some small variations on the frequency produce large changes in the phase constant. We can observe packages of dispersion characteristic branches when their cutoff frequencies closed to the metamaterial electric and magnetic plasma frequencies between 1.9 and 3.5 GHz. There are only three modes in the hollow core anisotropic metamaterial waveguide at the frequency range 1.4–2.8 GHz.