Today's technological needs are demanding faster and smaller optical components. Optical microcavities offer a high confinement of electromagnetic field in a small volume, with dimensions comparable to the wavelength of light, which provides a unique system for the enhancement of light-matter interactions on the nanoscale. However, further reducing the size of the optical cavity (from microcavity to nanocavity) is limited to the fundamental diffraction limit. In hyperbolic metamaterials, large wave vectors can be achieved. Therefore, optical cavities, created from hyperbolic metamaterials (HMM), allow the confinement of the electromagnetic field to an extremely small volume with dimensions significantly smaller than the wavelength of light. The goal of this thesis work is to investigate the behavior of HMM cavities for eventual comparison with experimental results. Type II hyperbolic metamaterials can be created from layers of metal and dielectric. A COMSOL axisymmetric model is studied to determine the characteristic lowest order resonances of whispering gallery modes within the cavities. This model is studied for silicon, silicon dioxide, and aluminum silicon dioxide layers. A setup has been designed for the experimental study of bulk HMM materials and HMM cavities. A discussion of the fabrication process for HMM cavities follows.