We investigate the interaction of polarized electromagnetic waves with hyperbolic metamaterial structures, whereby the in-plane permittivity component εx is opposite in sign to the normal component εz. We find that when the thickness of the metamaterial is smaller than the wavelength of the incident wave, hyperbolic metamaterials can absorb significantly higher amounts of electromagnetic energy compared to their conventional counterparts. We also demonstrate that for wavelengths leading to ℜ(εz) ≈ 0, near-perfect absorption arises and persists over a range of frequencies and subwavelength structure thicknesses.