Metamaterials are currently being extensively studied not only for their future potential applications in novel electromagnetic devices but also for the fundamental electromagnetic phenomena that cannot be observed in conventional media. Waveguides of metamaterial inclusions have been ones of significant research areas in metamaterials due to their potentials in near field optics and integrated circuit applications. In this paper, the guided modes along the circular air holes with dispersive metamaterial cladding are analyzed. The principal modes for each azimuthal eigenvalue are numerically investigated with varied hole diameters