Anisotropic metamaterials(MTM)can be used to control light propagations in emerging meta-devices and thus lead to various functionalities(e.g.hyperlens and cloaking).The tubular multilayered MTMs can work as optical microcavities,which exhibit very rich and intriguing resonance properties,depending on the constitutional materials forming the MTMs.Here we propose the exotic tubular cavities by using indefinite media with hyperbolic dispersion,which is in contrast to traditional anisotropic metamaterials with elliptical dispersion.In this tubular microcavity,the calculations reveal that it has anomalous scaling laws,such as the higher-order resonance mode oscillates at a longer wavelength and the resonant wavelengths hold their positions with changing the tube wall thickness and diameter.We also find high sensitivity in such anisotropic tubular microcavity.These findings can help the understanding of tubular metamaterials and could inspire interesting optical experiments and meta-devices.