Inside of a hyperbolic medium, the principal components of the permittivity tensor have opposite signs causing the medium to exhibit a ‘metallicbr’ type of response to light wave sin one direction, and a ‘dielectric’ response in the other. Our study shows that inside hyperbolic media, volume plasmon polaritons (VPPs) propagate along the characteristic planes, forming distinct, directionally dependent optical responses. This is similar to the propagation of conventional surface plasmon polaritons (SPPs) along the planar interfaces separating the isotropic dielectrics and metallic slabs. Interestingly, the plasmon polariton propagates along the resonance cone in a volume of hyperbolic metamaterial crossing the interfaces of the constitutive materials. The Young's double-slit scheme is used to study the spatially-confined diffraction in a hyperbolic slab, made of many thin planar layers of a metal and dielectric, to obtain the sub-wavelength interference pattern at the output interface. Proof-of-concept systems for producing such patterns applicable to nanolithography and subwavelength probes are demonstrated.